My opponent promoted to a King. Is it mate if a King is pinned to another King?

The official answer is that you cannot promote a pawn to a king, so this situation would never arise. However, this is Anarchy Chess, so let's set that aside.

If this situation did happen, and it is Black's turn, it is not checkmate, because Black's bishop takes the queen. It could not be White's turn, because there is no way to arrive at this board state on Black's turn without one or both kings being in check at the beginning of the turn, and so Black's move would have needed to remove their king from check.

Therefore, this board state is not checkmate.

The bishop is on strike as modern religious conditions makes his day-to-day services auxiliary and thus he will not attack until he gets paid
- One of the kings could still pay the bishop, so still not checkmate.

No, it's just hot.

Simply stack the two kings (after declaring "king me," of course). You may now move the stacked kings in any direction. If a piece, including a queen, attempts to capture the stacked kings, the demotion sound from Super Mario Bros. is played, the top king is removed, and the bottom king may capture the attacking piece.

Therefore, this is not mate.

Also, stacked kings weigh more and can thus squish an opponent

What century is this? When two kings want to mate, just leave them in peace unless you're about to consensually join.

If two kings mate each other they both die. The book says a thing.

This is called the “Bro’s mate” and was widely used in the early 1800’s.

It was widely used up until roughly the 1990s. Then they just came out and admitted to being in a monogamous relationship, as it was more publicly acceptable by then.
- It is now protected under the SCOTUS decision in the Obergfell case.

I don't see the issue with that bishop there.

My question is, can two kings and a bishop force checkmate?

Probably not, but a checkmate is possible if the white king works with black to make it happen.

Two kings can't touch each other smh

there's actually no rule of that
weird that you mention that, rather than the actual rule which makes this impossible, that you can't normally promote to a king. clearly OP found an exception to that rule though

Two kings, sounds like a good plan.