My family is also quite homophobic and very heated discussions often crop up in the house. Especially with this Chik-fil-a situation that has been going on. It usually degrades into a shouting match which then goes into religion and even into really deep politics.
At the end of the day, my family still loves me and I still love my family. It's not a big deal, they're people and they have opinions that differ from yours or even the majority of the world.
I guess what I'm trying to say is, deal with it. Just let them think what they want to think and you think what you want to think, because in the grand scheme of things... none of you will ever know if you were the right one, and it is very rare for someone to just change their mind.
At the end of the day, my family still loves me and I still love my family. It's not a big deal, they're people and they have opinions that differ from yours or even the majority of the world.
I guess what I'm trying to say is, deal with it. Just let them think what they want to think and you think what you want to think, because in the grand scheme of things... none of you will ever know if you were the right one, and it is very rare for someone to just change their mind.