but how can you show that denying gays the capacity to marry is NOT discrimination?

A church isn't exactly a private entity in the way a restaurant is, but discrimination of race certainly isn't tolerated anywhere. So why should discrimination of any kind be tolerated when marrying gays in a Christian church does nothing to alter the essence of Christianity?

I could understand your point if marrying gays somehow changed what Christianity is. Or if it somehow went against what makes someone a Christian. I, however, see know way that it does this.