I'm pretty sure that religious institutions are more-or-less unaffected by the law if they don't want to be. Prior to the law, they could put just about any requirements they wanted into agreements to wed people, like being part of the congregation, 9 months of marriage counseling (just in case!), etc., so I assume they can still deny Adam and Steve without worrying about getting sued.
I also like the not-subtle recitation of their state's rights being trampled on.

And of course, none of this would be an issue anyway if Christians hadn't muscled their way into violating church and state separation so their priests could be special little snowflakes and be state authorized to wed people instead of just keeping the two things independent of one another.

for the Cartoons and Animation subject tag.