Then the church will discipline him in whatever way it sees fit. It's not the business of the government. Separation of church & state is in the U.S. Constitution.
In the reverse case, when an Episcopal pastor in my town refused to accept that he had a gay married bishop, which is OK in the US Episcopal Church, and his congregation went along with him, the Episcopal church ended up repossessing the church from that group (because in the Episcopal Church, the denomination, not the congregation, owns the building.
The pastor & congregation affiliated with the Episcopal of Africa, which does not allow same-sex anything and is one of several groups at the heart of the criminalization of being gay in Nigeria. The state & US government have no right to do anything about that either.
The Supreme Court refused to take the case, because it's the church's business and not the state's nor the federal government's business.
If a Catholic priest married a gay couple, probably he would be excommunicated (and fired, of course). None of that is the federal government's business.
Here's an Australian priest who got excommunicated just that way.
If it happened in the US, the government wouldn't and can't legally intervene.