interesting idea...
Compulsory Capture Variant

@spacebar I like the name munchers chess most, and I think if the only thing stopping you from capturing is being in check then it should be checkmate to make it easier to blunder checkmate.
So for instance
in this case white would be checkmated in the final position as the check would be the only thing stopping white from capturing the pawn.
And in this case white would have stalemated black as the pin would be the only thing stopping black from capturing the pawn.

disagree with the 2nd example, black has no capture move (as the N is pinned), so he can just move his king.
Not allowing non-captures when in check, well it just makes the game really, I dunno, different, I'd say unintuitive, difficult.
I don't like it, and it doesn't make sense either. When in check your only legal moves are ones that get you out of it. The fact that you'd be able to capture some piece if you weren't in check, is irrelevant.
Another topic: any color promotion, wouldn't it make more sense to only allow promotion to enemy pieces? Otherwise it's kind of pointless (unless you are in some very akward situation. Or it's giveaway)

Another topic: any color promotion, wouldn't it make more sense to only allow promotion to enemy pieces? Otherwise it's kind of pointless (unless you are in some very akward situation. Or it's giveaway)
Yeah that makes sense. Normally if one could promote to their own color promotion to an enemy piece would be a blunder so that people would seldom promote to enemy colors unless that was compulsory.

Why not promote to your own pieces like normal chess?
And I agree with spacebar with check moves. The game should be that you have to do any LEGAL captures you can.
Let me elaborate on the issues of having legal non-capturing moves allowed in case of a check:
1. I blundered a move and blue of course is allowed to checkmate me, but I am not mated and blue is forced to capture my own pawn, so I'm already up in material. Ergo: as long as players are not mated when they have a capturing, illegal move but still can play non-capturing move, it is nearly impossible to mate them as long as one does not have a great material advantage.
2. Thing two, it encourages passive play. The variant is passive by itself, but having such quick mates is something that makes it interesting and play-worthy: this thing should be kept. Otherwise we could see std FFA with endless shuffling for 200+ full-moves, or very boring std munching teams games were this played with standard.
3. Thing three, to have such mates prohibited goes against the concept and even the name: if it is munching chess, you always have to capture pieces. Think of it like this: black checks white, white captures a piece, black captures white king. White king cannot avoid the king capture without playing a non-munching move, therefore white is forced to play non-munching move under current implementation. Feels weird, right? In munching chess you have a capture but are forced to play a non-munching move: take for example Giveaway + KOTH, you are forced to capture, even if you can win in one move via KOTH. However, the same reasoning does not apply here for some reason under current implementation..? Same thing with RB giveaway teams, you can stalemate the teammate with one pawn move, but you may be forced to capture the opponents' last pawn first.
tl;dr: when in check, and one has a capturing move that does not stop the check, that should be a mate. Otherwise game is too dull and does not go with the logic of giveaway-style forced captures. I'm not allowed to KOTH here, I'm not allowed to stalemate my teammate in stalemate wins here, but I am allowed to stop myself from getting mated? Weird, right?

FYI this was super easy to code (given we have giveaway..), so i added it.
it's also easy to remove the getting out of check logic again, if we really decide that's what we want.
you can test it here
https://www.chess.com/variants-test/munchers-chess/analysis

Well I think at least in Capture the King or Fog of War combined with Munchers chess non capturing moves shouldn't be allowed even when in check as in both variants you can legally move into check anyway, and being able to make non capturing moves in Fog of War lets the player who is in check know that they are in check.

Well Bab decided it's better to have it as originally suggested, and bstri agrees, if you're in check and have a capture that doesnt get you out if it, it's mate.
I think the name munchers isn't appropriate in that case, you dont really get to do much munching. So i'd suggest we call the rule "Forced capture" (i think 'forced' is easier to understand for most non-english speakers, than 'compulsory'

I think if you aren't in check and the only reason you can't capture is that capturing a piece would be moving into check then it should be stalemate as that would make for some stalemate traps not seen in standard chess.
For instance after white plays Kh4 black should let the h pawn get taken and promote the a pawn as if black plays Kg6?? then white is not in check but the only reason white can't capture the h pawn is because doing so would put white into check.

Also I noticed that if the king is in check and the king is the piece, for which the only reason it can't capture is that doing so would leave it in check then it's not checkmate.

Also I noticed that if the king is in check and the king is the piece, for which the only reason it can't capture is that doing so would leave it in check then it's not checkmate.
what?
Right now there is already a variant, Giveaway, in which capture is compulsory, but in Giveaway you win by capturing all your opponents pieces. I think it would be interesting though to have a variant, in which you win in the same way as in regular chess, but if you can capture something you must.
So for instance in this variant if white played e4?? from the standard starting position, black could immediately win the queen with h5 as the queen would have to take the pawn.