The CHURCH (or churches, really) can deny whatever rights they want, just as they can believe whatever they want, no matter how outlandish those beliefs may be. After all, they already decide who has the right to God's blessings and entrance into heaven, etc... See More.
The STATE does not have that same right to deny rights and privileges from one group of people that it allows another. Queer folks who want to be married in a faith-based ceremony can find religious communities in which to be married, but citizens need equal rights. (This is why I am in favor of NO marriage licenses for anyone).