I'd tell you good for you.
I was, in my younger years, quite active in my church. Full of good people, and generally speaking it was a rather contemporary church, theologically speaking. The "procedures" were rather conservative (which I like...I'm not much for singing, as I suck at it, and I do like the sermon), but the theology and teachings were in line with what I personally believed. I miss that.
When we moved, the church we found was...shall we say...highly conservative, in matters of theology. The same type of thing you seemed to have experienced, if I'm reading you right. It makes me sick, and has done nothing but continually hammer nails into the coffin of my religion for the past...4 years now? I'm not sure what I consider myself to be religiously anymore. lol Before I prattle on and make this about how bad my own church sucks, rest assured, you are not alone.

I don't tolerate hate, particularly backed by religion, towards any group, even if the group is not my own (I myself am straight).
Speaking to you, good for you for standing up for yourself.

Condemnation of homosexuality is, in the Christian context, horribly misconstrued anyway...if you'll look, quite literally, within five lines of the "prohibition" against homosexuality, you'll see similar condemnations against the cutting of hair, eating shellfish and pork, tattoos, and wearing clothes made of two different materials. I promise you, it'd be an interesting conversation piece next time the pastor walks in with that polyester blend on.
Do you "have" to tolerate it? No, not at all. I "tolerate" my church only for the sake of my seven year old sister and my mother...I don't want to ostracize them for my own beliefs. I would tell you that you haven't lost anything in them anyway. People, in both the best and worst of intentions, can and will misconstrue the Bible to say whatever it is they wish. Don't allow what one reading of the Bible is shape what it "is" or "should" be for you. In this case, I'd tell you to ignore the hell out of your cousin...unless he'd like to debate the matter over a shrimp cocktail?
Do hope I was of some help...don't let them get you down.
Hugs,
Harley