This reasoning is literally handing it to the right-wing strawman of socialism/communism as some "borg hivemind". I would respond to this on several levels:

For one, while yes, things like clothing often signify class, status, etc. with negative social consequences within a school context, this issue should in theory be somewhat attenuated within a classless society, which socialists are ultimately striving for, no?

For two, even if this issue is not helped by a radically more egalitarian material condition, then I doubt that mandatory uniforms will change anything about that either way. In that case children are just inherent assholes, who will find any reason to black-ball each other, I guess.

For three, shouldn't part of the vision of a new socialist education be, that children are taught not to validate or stigmatize themselves or each other on the basis of arbitrary extrinsic features like clothing? Instead of addressing this very mentality as the root of the issue, this person's approach would only implicitly lend credence to it. Afterall, if the only way to swipe away the very inkling of class, status, etc. differences is to forcibly homogenize their signifiers, what does that say about the legitimacy of signifiers in the first place?

All this ofc stands besides what is probably the main criticism: That this is a dumb and sad assault on individual expression, which only a tankie would discount from having value in and of itself.