Not sure if it’s necessarily a ‘conservative’ thing - in the UK (and maybe elsewhere) a lot of schools have uniforms, partly as a way to engender a sense of togetherness/community and partly because if everyone is wearing the same clothing, then socioeconomic differences aren’t so visibly contrasted by some kids wearing designer gear while others can only afford the less expensive stuff.
From that point of view you could see it as being quite an egalitarian idea - although the availability of affordable uniform is still a potential issue, and it’s important that lower income households are able to get the right clothes within budget.