Be2 maybe?, 4... g5?? would blunder M2
How to stop this?

Play bd3.
Although g5 isn't a particularly scary move. The bishop is still useful on g3 because bishops are long range pieces.

I just want to point out that 2...Nc6 and 3...f6 are like the two worst moves that you could play without blundering anything. Follow DaBaby's line, and their king also get stuck in the center.

Play Bd3 threaten Qh4+ force the king to move then play a3 or c3 to stop Nb4. When you don't play e3, you still don't bring the bishop back if it's attacked, that's basically avoid being passive by being even more passive

As a main london player myself, I don't see any problem with 4.g5, I would simply move my bishop to g3 after it, since, contrary to what you say, i consider that the bishop isn't being pasive at all, you can see that it occupies the entire diagonal, i would just tell you to not block your bishop with your other pieces, and you should be doing ok. And regarding to how you should play the opening, I would recommend you to play 3. Nf3, instead of 3. e3, that's what I do, because it is more flexible for me, for example, if i play against a King's Indian defense, I prefer to play the pawn to e4, and take the whole center, whereas, against d4 d5, i play the pawn to f3, and try to play for a close center. I hope this helps you, now I am going to put some of my games to see if that helps you.
In my games played of London system (about 5 or 6), I witnessed in about half or so of these games this very stupid move that I want to counter and not be passive and put my bishop in a hole.
Here:
Or I don't play e3 at all and do this: