You gotta admit four guys singing girl songs and going "oooh" could be seen as sexually ambiguous for the early sixties. Not that there's anything wrong with that. Even Elvis swung his pelvis in a way that female strippers did the bump-and-grind. I think on some level there was a fear of Elvis and the Beatles as loosening our Anglo-Saxon sense of manliness (which we got back with metal bands like Judas Priest, uh, oh, forget that reference.)
Let's face it, Brian Epstein was gay and attracted to the Beatles and essentially dressed them up like dolls in suits as some kind of marketing/homoerotic fantasy.
The "gayness" of the suits (compared to their leather gear--which is totally gay if you watch some of Kenneth Anger's movies from the period) probably was part of the reason John hated them.
I don't think the Beatles were personally gay (with the exception of John's sexual confusion), but their Beatlemania image projected a certain effeminacy/objectification/doll-like-ness. Just look at the cover of "Meet the Beatles". Four little disembodied heads on display like cadbury chocolates.
I think by 1965-66, the Beatles had successfully shed the early effeminate image and were writing original songs like "Run for your Life" to show that they were real, women-beating men.
Complex issue, if you want to be honest about it.
I hope Velvet Underground and Nico made the list, because that is the most gay album cover of all time. Sticky Fingers coming in a close second. Both by Andy Warhol. I wonder how he would have done a Beatles cover?