AITA because I don’t want a rainbow/LGBT flag in my living room?

ESH a bit, she was wrong to jump to "you're a homophobe for taking down my flag" (said respectfully as a queer person), but it sounds like you're not giving her enough input in your shared apartment.
Just the opening phrasing "I am currently sharing my apartment" - once you share, it's no longer your apartment. It's 'our apartment'. You have to make concessions and allow other people to have some input in their living space, otherwise you're treating the shared spaces like they're not shared. I get it, I'm a very particular person and I currently share with 5 other people. It's hard, I don't like how messy people are, how they leave their stuff laying around. But I have to deal with it, because we're living together.
You could've approached the situation in a different way too, suggest she hangs the flag from a window in the apartment and say "hey, it'll make much more of an impact if more people than just us can see it?" - that way she can hang her flag, you get the living room to be flag-free and you'd be making a move as an ally.

/r/AmItheAsshole Thread