Jamaesi, unfortunately, it is the right of any church, or denomination, to set rules for it's membership, leaders and rites. They have the right to discriminate against anyone they wish in marriage, funerals, etc. We had a church here recently refuse to marry a couple because, although she was a widow, he had been divorced. This is a Christian, and not Catholic, church. They can do that.
The government, however, in my opinion, cannot discriminate in any way. So, now that the sodomy, etc. laws have been struck down by the Supreme Court, human rights are being violated every time a same sex couple is refused a civil marriage license or civil ceremony. THAT we can change in time, and will.
For the religious part, you will have to find a church whose polity allows it, or find a minister who will do it anyway. I have done it for people and will again, but my state has made same sex marriages illegal, so I call them commitment ceremonies and do them.....but they have NO legal standing. That all goes back to the government part of the puzzle. I think whatever they call the licenses and legal unions, it should be called the same for all couples, and the churches can do what they want....it's called religious freedom....however much I disagree with the stance of those who say it's a sin or not allowed by God or whatever. It's the legal end of it that ensures benefits, survivorship rights, etc....so THAT is where we have to start. Hopefully, religious organizations will follow in time.