Well, if the root of the fear of gender variance
is homophobia, my guess would be it's because everyone seems to find androgyny a little hot.

aaand, I think that scares some people when they realize they're feeling attracted to the "wrong" gender. Post-surgery I've caught people checking me out from all sides now; straight men, gay men, gay women, straight women, both cis and trans. Does a number to my ego.

On the other side of the coin, that means gender-variant people are on the frontlines though, man. I was a "straight-looking" and "-acting" lesbian for 10 years before I started thinking about gender. Deeply involved in evangelical Christianity at the time, I was really annoyed with the feminine men and masculine women who gave gay people a "bad name;" I wanted homosexuality to be associated with "normal," God-fearing, khaki-wearing, child-rearing church folk, not the hooligans who wore dog collars and danced around in the streets in their underwear.

It took me a long time before I stopped judging and started celebrating the gender diversity within our community. It took me even longer to realize I didn't know my place on the gender spectrum as well as I thought I did.
Now I'm the one that many cis gay folks - and some binary trans folks - want to disassociate themselves from, because I don't fit. I give both gay and trans people a bad name by association because whether it's orientation or gender, I'm clearly "doing it wrong."
If I could go back in LGBTQ history, I would orient our movement around gender variance instead of attraction. Instead of pouring so much energy into convincing people that men can love men and women can love women, I would broaden the scope to tearing down the boundaries that defined men as men and women as women in the first place. With those categories dismantled, freedom to be attracted to whomever you happen to be attracted to would follow naturally.