There is nothing stopping someone with particular beliefs (for example, being against homosexuality) from politically supporting gay marriage if they so choose.
Sure, it is awkward and contradictory, but people are free to make choices. Somebody who believes that homosexuality is a sin is not forced by any moral, political, psychological, or religious factor to oppose gay marriage.
I believe this question has different answers depending on which denomination of Christianity you say you are a part of. Now I am not a Christian but I was raised a baptist and have read through 3 different versions of the Bible and it is my belief that the majority of Christian beliefs would say yes you can support the legislation for LGBT rights but not the morale lifestyle of homosexuality.
In terms of marriage, I would have to say no. God created and defined marriage and I don't see how a Christian can justify believing the bible, yet being okay with a government redefining God's Word. Government is ordained and authorized by God, but if it acts outside of his express will then it is not authorized.
HOWEVER, I do believe that homosexuals do have a right to life, liberty, and the pursuit of happiness within the bounds of the law like anyone else. They are not to be jailed just because they have a different sin problem than others. Let's remember that everyone has certain proclivities to certain sins. Just because someone's is different than mine does not make them worse than me or you.
Christians should not be hypocrites. You either support homosexuality or you don't. If you support gays politically, in what way are you opposing homosexuality in your heart? That is like not wanting your child to smoke but allowing them anyway to "give them freedom". As a Christian, I'm against gays because it is a sin no matter what.
If you support it politically and let people be homosexual more and more people will think that it is ok to be homosexual and will be in term be led away from god. It needs to be against the law to do this and "gay marriage"should not be a thing in terms of being a valid documented marriage,for tax purposes