“And lose tax exempt status. We’ll see who is willing to do that.”
In the short term, I don’t see it happening. In order to solemnize “marriage” licenses the church or pastor has to actually ask permission from caesar to do so. So not only are churches the unpaid agent of caesar, they have to ask for the “privilege.” There is an easy way to avoid doing that: don’t ask permission, or return the permission if already granted. There may be a few unwise churches who get caught out, but once that starts, you’ll see churches simply refuse to solemnize “marriage” licenses at all.
Long term of course the objective is to have all churches answer to caesar regarding doctrine, etc. Those who do not will be persecuted. There are plenty of churches flying the rainbow flag already. I don’t see the overt persecution happening for awhile.