I've never felt weird about eg Madame Doubtfire.
Mrs Doubtfire was obviously still Robin Williams. The cinema audience knew that. The joke was that the family couldn't see it, despite it being obvious. I haven't seen the film for years but IIRC the narrative is very similar to other stories where a character disguises or hides themselves in order for others to be able to "see" the real person underneath the costume (a bit like Cyrano de Bergerac).
Plus Mrs Doubtfire was an affectionate portrayal of a woman, not a sexualised stereotype of what a man thinks a woman "should" be like.
I do find drag a bit difficult, but again I think there is a qualitative difference where a male performer dresses up as a woman and tells jokes.
On the homophobia thing, homophobia is hatred of someone because they are gay/lesbian. Unease with a man wearing a woman's "skin", making himself into a grossly sexualised stereotype of a woman, has got nothing to do with his sexuality. We don't even know his sexuality.
Plus - Silence of the Lambs.