Relative pronoun

Yes. The transitive sense of think is rather formal in AmE, so I would use whom.

AG, I've gotten a bit confused. Are you saying this one is rather formal (but still works fine)?

He is the man who(m) they think a great musician.

I'm saying that They think him a great musician is formal in AmE, so it would be more appropriate to use the more formal whom in your relative clause.

AH! I see. So this one works as a formal English, right?

He is the man whom they think a great musician.

Yes.

Good! Thanks, AG!

AG, let me confirm. Do you think even If "whom" was omitted as this, it would still work?

He is the man they think a great musician.

Yes to your last question.

And I'm not sure why Aspara Gus is telling you that 'whom' is "formal". It's just the object form of 'who'. She is the woman to whom I gave the book.

So "he is the man who they think a great musician" is simply ungrammatical.

There comes a point in the progress of a language through time when a use becomes so moribund that strict adherence to the established grammar norm becomes a de facto error. "Whom" is indeed the objective case of "who", but its use outside of certain fixed expressions and when it does not immediately follow the preposition has become hypercorrect, or at the least highly formal.