I don’t think that’s it with the gays, exactly. For most people it’s the principle of the thing, I think. Secondarily it is to use the state to force normization, which is more important for nonpolitical reasons. Finally, the “LGTB community,” which is not whatsoever an actual community, is just another identity group useful for pushing a panopoly of leftist interests, gay “marriage” being a useful wedge issue. See how it alienated young adults, for instance, from the Republican party, without them being interested whatsoever on a practical basis.
Finally we get to what you’re talking about, and there’s that. There’s also probate law, presumably, concerns over property, contracts, adoption, etc. There are so many ways the state touched our lives, and who has the time or patience to de with everything line by line? Easier to fall into readymade arrangements and classification. And it’s close enough, they think, since marrieds also cohabitate and have sex (sometimes).
But I still think it’s mostly what I said before.
Bottom line:
Small government = no religious freedom paradox.
Big government = complexities and contradictions impossible to set straight.