Somebody put forward in another thread that homophobia is the last socially acceptable form of bigotry. Homosexuality gets all the attention because it has a human face, and is a fixed group toward which hatred and bigotry can be directed. You couldn't satisfy the tribal human desire to hate / punish / oppress / feel superior toward a group of outsiders if you went up against shellfish-eaters, lepers, menstruating woman-touchers or beard-trimmers instead of homosexuals. All these things are also abominations - some of them, like the rules against touching menstruating women, get more airtime than sodomy.
So why is it that homosexuals such get a thrashing while Christian women get to let their hair hang loose in the chapel and eat rabbit and shellfish? They're an ostensibly identifiable group. A Christian woman might wear a hat one Sunday and not the next, and a Christian man might have sacrilegious bacon for breakfast and wholesome beef for lunch, but a gay person is gay morning, noon and night. Humans love to hate an identifiable group. It's just the sort of thing Jesus came to earth to put a stop to, and IMHO he would heartily approve of your moral strength in standing up for your cousins against the petty, blinkered threats from your fellow churchgoers.
I am thinking, though, is this really a "choose between your faith and your family" issue? I mean, being gay is not a choice, but attending an anti-gay church is certainly a choice. Have you been to church with your cousins? Maybe their church would be more in harmony with the ethical fruit of your own personal relationship with Christ.