What an outrageous opening
Defending the Pawn Wall Opening

Mirroring pawns is not a strategic aim. You wouldn't play g5 if they hadn't played g4, so why play it when they do?
2...d5 works well here, but more general advice when people are making lots of pawn moves:
- Don't develop pieces where they can be kicked by pawns. So I wouldn't play ...Nf6 in your game after g4. I'd develop the dark-squared bishop first and play Ne7
- Beating these guys is like eating a coconut. You have to smash the outer shell to get to the tasty treats inside. This is the bit I see beginners struggle with, because very often smashing the pawn barricade open involves sacrificing material. At your level I wouldn't advise sacrificing pieces, but often it's a good idea to sac a pawn if necessary to open the position up.
This opening apparently has no name. I've lost to it at least once, probably several times.
https://www.chess.com/game/138650008646
The experts scoff at how useless it is. Well I've lost to it enough times that I'd like a strategy for fighting it.
Like you said, the key is to not allow it to happen in the first place. On move 2, ideas like 2...d5 and 2...h5 are much better than mirroring whites plan with g5. That leaves yourself with light square weaknesses on the kingside and less opportunities to crack open whites position.
By move 5, you leave yourself short of good pawn breaks and the ability to take advantage of whites lack of development.

Well, the remedy to this "opening" is really simple: Don't throw away your pieces.
9...h5 blunders a pawn.
11...Nxg4 blunders a Queen.
18...Rxh3 blunders a rook.
But the biggest blunder is certainly 5...Bxg1. White has weakened a whole complex of dark squares, and in response you punish him by exchanging your perfectly placed dark-squared bishop for a knight that has not moved, and doesn't even have a decent square to sit at.
This opening apparently has no name. I've lost to it at least once, probably several times.
https://www.chess.com/game/138650008646
The experts scoff at how useless it is. Well I've lost to it enough times that I'd like a strategy for fighting it.