That's the rub isn't it? We aren't talking about the govt preventing anyone from doing something. We are talking about whether the govt should official recognize it for whatever reason. Not the same thing.
I'd argue that the government has no right to regulate marriage, period, and I think religions are flat out insane for not going completely bonkers over it. But that's me.
IF government is in the marriage game, for good or ill, equal protection under the law applies. The government should have a really high bar on telling one group of folks "Yes, I shall grant you this shiny special status" and tell another group "Nope, I shall not grant you this shiny special status". I can understand religions getting honked off at the cheapening of marriage, especially in the face of divorce rates these days.
But what's the justification on civil unions that aren't the modern version of miscegenation laws?