Paul McCartney

To get the Fe vs Fi argument out of the way first I will start with his which Feeling he preferred.

Your mileage may vary, but one point in favour of Fi I would highlight would be in this interview here (seriously, check it out): https://youtu.be/ufor1B9y7Xw. I know Fi generally keeps to itself more than Fe, but, all else being equal, Fe can also be a bit more deliberate about what it reveals, whereas McCartney just kind of said stuff in the moment without considering how it made him look. I don’t think McCartney filtered everything through the prism of ‘How is this going to affect others? How is this going to make me come across?’ I think he was more just true to himself and let the chips fall where they may. I did consider Fe for him but I think that's just because he was a kind of a agreeable person (in a Big Five sense). If we take it that he has Fi, then his advocacy for farm animal rights was stemming from an internal value than external one, i.e. not primarily orienting his values by objective sentiments/data, but rather they sprung from inside, passionately. Fe types can definitely advocate for farm animals, too, and, yes, doing so is definitely an 'objective value'. But for the reasons I mentioned, I think McCartney fits the bill for an Fi type better in this context.

Argument for ESFP (I will present the argument for ISFP later):

Now to the meat and potatoes, ISFP or ESFP. I will start with Ni. So as I understand it best, the Ni quality is something that ESFPs find to be very taxing on their mental processes (as all inferior functions go). Ni, while can be understandable to them, simply gets in the way directly perceiving the object, object not being limited to just sights or sounds (though those apply primarily) but also just the natural flow of life i.e. the things one needs to do, places one needs to go, and people one needs to see. Thinking "Ni stuff" takes up too much time so it gets pushed to the wayside until some someone directly wants to bring up some philosophical conversation in which it will be up to the individual to decide whether to engage with it or dismiss it (as there is variance in this department).

Ni in ISFPs work a little differently. As I understand it, the ISFP brings the symbolic representative nature of Ni into union with Fi and Se often by expressing itself through some aesthetic form (and by "aesthetic" I'm not limiting it to "art" but also a way of life or a way of carrying one's self). Tertiary Ni in the ISFPs can cause them to have a tendency to want to and try and capture the "beautiful image" based on their perspective like the following:

Frank Ocean: "When I'm trying to make a song ... I'm trying to make a photograph out of something you can never see."

Leni Riefenstahl: "I [seek] a style in the realm of legend. Something that might allow me to give free rein to my juvenile sense of romanticism and the beautiful image."

Now, I have to preface that it does get tricky as because it's tertiary, meaning ISFPs can toggle it on and off, so many ISFPs will be realistic (meaning not concerned with the "ideal") in many things whilst in some others things they will be. But all else being equal, an ISFP is more likely than an ESFP to express an object or their work via subjective associations and impressions, as a results of higher subjective Feeling and Intuition, and lower Sensation and Thinking, than the ESFP (along with introversion). McCartney fits the latter than former:

McCartney: "I don't ever write a song thinking, 'Now I'll write a song about...' I do sometimes, but mainly I don't. Mainly I'm just doing a tune and then some words come into my head, you know. ... It doesn't mean anything, you know, but those just happened to come to my head. So that's what this song is about... it is about my dog. I don't mean it, you know. I don't ever try to make a serious social comment, you know. So you can read anything you like into it, but really it's just a song. It's me singing to my dog." [Source: http://www.beatlesinterviews.org/db1968.1120.beatles.html]

McCartney: "There's nothing deep behind a scream, you know? A scream is just the same as a roar in a football match; there's nothing, sort of, sexual or any horrible things like that. You know, that's the sort of thing people occasionally read into it. There's nothing like that in it, I don't think, because when I used to go to shows, I'd shout—but I didn't mean anything more than 'I like the music you're playing' or 'I like the way you play your guitar,' sort of thing. There's nothing behind it."

Contrast this with how ISFPs describe their work, one can see that they imbue to a noticably higher degree, using Ni to serve Fi in taking a deep inner emotion and finding a singular, symbolic archetype to represent it:

David Bowie: "[My paintings] are very personal to me as well. They're all portraits, and they're all portraits of people in isolation. Most of the paintings are Germans or Turks who live in Berlin, and they're either from East Berlin and who are now living in West Berlin and knowing their family's on the other side of the Wall. And so, I try to capture a lot of that kind of isolation, and I put a lot of myself into paintings as well; they're very much part of me."

Frank Ocean: "I was just trying to articulate visually the feeling of being numb—like the feeling of somebody trying to love you but you can't feel it, like the feeling of wanting to feel something that you can't feel. And so it's numbing, and a lot of things can cause that numbing. And in the video, though, it was like some sort of topical anesthetic and a little bit of special effects." 

Now the argument against this will be that the ISFPs I mentioned had (or has, in Frank Ocean's case) highly developed tertiary Ni, and so by nature were more more introspective than other ISFP individuals. And that isn't a terrible objection but now let's compare him to a more "Se" Fi-Se individual in Avril Lavigne then (whom almost no one would object to being less Ni than the other aforementioned ISFPs):

Avril Lavigne: "I write a lot from my personal experiences in life—either situations, emotional, very emotional things that I've been through [that] I've experienced; situations that really get to me [or] move me; how I feel, maybe, about other people; other situations I've seen my friends, my family have gone through. And my songs are open for other people's interpretations, and I think that's the beauty of music. ... I just think that's really cool: to throw my own emotional experiences to a song, to use music to express myself, and then have people around the world check it out, hear it, listen to it, and have it mean something completely different to them. ... I know I can be going through something one day and hear a song come on the radio and totally be like, 'Yeah, I'm feeling that way right now.' It makes me feel empowered, or it just moves me emotionally."

So as shown, even compared to a more Se-heavy ISFP Avril Lavigne, McCartney seems to view things on their own terms to a greater degree as a result of experiencing the world as object (the extrovert, which in this case McCartney) as opposed to a dominant Introverted Feeler primarily experiencing and orienting the world and things through the lens of their own subjective emotional depth (in this case Lavigne). 

Now, this does not mean that extroverts will not try to imbue things with subjective depth, one could find many examples of EFPs doing that (as a result of auxiliary Fi), no one is a pure introvert and extrovert afterall. However, if we agree that McCartney, by comparison to others ISFPs, does not exhibit such a subjective layer between himself and the object (i.e. does not feel the need to tether the object to his own subject as a primary source), then the likelihood of him being ESFP is stronger. 

To move on, I'll further explore his function stack. Fi dominants hate having to make real-world tradeoffs that compromise their ideals, EFPs too of course, but IFPs to an even greater degree. It's just a matter of degrees. McCartney doesn't seem to have the IFPs tendency to either want to hold/experience a personal ideal/sentiment to the purest extent or trash it entirely. Rather, he seems more willing to compromise purity of Feeling in specific ways in order to get a job done, or get a personal project out into the world, (which doesn't sound like dominant Fi):

John Higgs: "McCartney places great emphasis on starting and finishing work immediately, before you have had the chance to overanalyse or come up with an excuse not to do it. ... As he explains, ‘you get rid of the hesitation and the doubt, and you just steamroll through’. This approach paid dividends when he came to work with John Lennon. Every time they sat down to write a song they would finish it, and they never once came away from a writing session having failed to come up with something. 'I’m all for that way of working,’ he has said. ‘Once John and I or I alone started a song, there was nowhere else to go; we had to finish it.’"

Contrast this with the ISFP Dido, whom prioritizes inner harmony and alignment above all:

Dido: “[The way] sort of been the way I’ve been with everything in life [is] if I’m not feeling like I want to put the music out, then I won’t put the music out. Or if I’m not feeling the need to get up on stage, then I won’t get up on stage.”

Dido: “People keep saying, ‘Why did you step away [from making music]?' It didn’t really feel like that to me. I just write songs. ... I’ve never made records until enough of it builds up and I feel like I’ve got something to say."

I would like to provide more cognet arguments on Paul McCartney being an extrovert and not a introvert but it is always hard to prove a negative. However, in arguing the primacy of Se in McCartney's psyche (and general extroversion) I would like to submit the following quotes attesting to his general extroverted attitude:

McCartney: "If I was to sit down and write a song, now, I'd use my usual method: I'd either sit down with a guitar or at the piano and just look for melodies, chord shapes, musical phrases, some words, a thought just to get started with. And then I just sit with it to work it out, like I'm writing an essay or doing a crossword puzzle. ... I've really never found a better system and that system is just playing the guitar and looking for something that suggests a melody and perhaps some words if you're lucky. ... But I'm of the school of the instinctive."

McCartney: "There is no sort of point you just think, 'Okay, now I can do it, I'll just sit down and do it.' It's a little more fluid than that. ... It's this fluid thing, music. I kind of like that."

Another important thing is that, as extroverts, ESFP in a general sense, will be more 'on the go' than ISFPs (not a rule but it is a indication) due to a (again general, not universal) dislike for humdrum environments in the EP temperment. Of course, typology is cognition and not behavior, but it gives certain clues:

McCartney: "I've just been on holiday for three weeks ... After three weeks of that I get bored, I wanna meet people again and get back to the life where you're sort of meeting people every second. ... This is a change from having a restful life, I'm not very keen on this life where you sort of blaze around in the sun, can't stand it."

The counterargument against ESFP is that some of his songs contains metaphors and the like, that there is more to his work than merely the sounds but that could also apply to many other ESP artists. Is the average ESP supposed to say their film meant nothing, people shouldn’t read anything into it, and doing so isn’t evidence of their having deeply engaged with it? As Ric Velasquez said, "Do you expect lyrics written by an S type to be completely devoid of all metaphor and abstraction? And if so, do you also expect the lyrics of N types to be completely devoid of all practical and specific meaning as well?"

Argument for ISFP:

For starters, metaphors in his songs like Blackbird and it's connection to the civil rights movement definitely seems much more semi-conscious Ni than unconscious. All else being equal, an ISFP is much more likely to channel that type of abstraction to their work than ESFPs (not that an ESFPs work is automatically more shallower or anything). As IDRlabs said, an inferior function can't just be developed in the way of dominant, auxiliary, of even tertiary, because it's the polar opposite of the dominant, so it becomes repressed, a horse which cannot be educated.

Also, an ISFP is typically less disclosing of the abstract meaning of their work. Ni in itself often finds it difficult to explain itself, and so does Fi by itself (the 2 introverted "idealistic" functions), so when one has both functions and none of those 2 functions are repressed, then the Fi-Ni comination makes self-expression particularly difficult. Which could explain this quote:

McCartney: "I don't like people explaining albums. The only way you can explain it is to hear it. You can't really use words about music, otherwise we'd do a talking album. The album is the explanation, and it's up to you to make sure what you want of it."

Not explaining their work is something very common among ISFPs in general due to the combination of Fi-Se-Ni as shown below (Yes, ESFPs can say they don't like describing their work either but just from my observation, they are generally more talkative and open):

David Bowie: “I had to resign myself, many years ago, that I’m not too articulate when it comes to explaining how I feel about things. But my music does it for me, it really does. There, in the chords and melodies, is everything I want to say. The words just jolly it along. It’s always been my way of expressing what for me is inexpressible by any other means.”

Kate Bush: "I really like the idea of my work speaking for me, not me speaking for me. I think my works says a lot more interesting stuff than I ever could and it’s more eloquent, and that is what I feel I have to offer the world. I don’t feel that what I have to say personally is that interesting and it’s not something that I have enthusiasm about, it’s not fun for me – I don’t really enjoy it."

So looking at it from this perspective, we can chalk up all the examples of dominant Se for McCartney as auxiliary Se expressing itself to protect the private nature of Fi-Ni. Remember ISFP's main perception function is Se, Ni is subordinate to it, it's just not relegated to the extent of Se dominant.