I think constant moral judgment can have a chilling effect. But to throw it out altogether is not the solution (it’s certainly not working at 4chan).
Claiming that everyone has their own morality is only true in the sense that no two snowflakes are alike. It may be correct at the molecular level, but snowflakes are more similar than they are different. So too with human morality. Mine may be slightly different than yours, but the overlap is huge and consistent.
I think perhaps more importantly (and the reason I made the comment in the first place), morality is contextual and easily influenced. If we never talk about it, no one knows what sorts of behaviours are appropriate. So I talked about it to put a peg in the ground. You may disagree and that’s fine. You drive your peg in to the ground somewhere else. But knowing there are two pegs is important.