I'm not involved nor have I ever engaged with the "Gays For Palestine" movement, but I can give my own answer as to why I, a lesbian, support Palestine.
Basically, I don't think people's right to a safe place to live is dependent on whether or not they support gay rights. I would love it if Palestine could move in a more tolerant direction, of course, but they need to be alive to do so. I don't think civilians deserve to be bombed, homophobic or not.
I admit, the argument that gay people shouldn't support Palestine because Palestinians don't support gay rights always annoys me; do people really have such minimal empathy as to assume that I'd throw innocent civilians under the bus and change my mind about their right to safety, food and healthcare just because they are part of a homophobic culture? I, and I imagine many others, are well aware of the lack of gay rights in Palestine already; it isn't a "gotcha" when that is already common knowledge, it just doesn't change my opinion on basic human rights.