Actaea

Unlikely. Seriously, I often see such arguments, but I've never seen children compare clothes. Phones, as Ples suggested, maybe. Clothes? That's just ridiculous. On the contrary, the more tattered your jeans, the more authoritative you are; it's obvious.
So, rather, they grow up narrow-minded and insecure because they can't wear what they want.

When I was in school, mobile phones didn't exist yet. Well, not for us, the students. I think I got my first one in tenth grade.
I didn't quite mean that when I talked about clothes. Children will always find something to tease or bully others about. Whether it's different clothes, a surname, hobbies, a reaction, or anything else.
But if you take the situation: uniforms are introduced. And a poor family buys this miserable jacket and trousers for half their salary, while a rich family buys them without a second thought. But the children look the same. This possible psychological barrier is eliminated, that "he's different, not like me." The stratification is partially smoothed out.
I'm not saying that all children bully each other because of clothes, not at all. But if there are even 5% of cases where "we won't be friends with you, you're dressed like a bum," then uniforms will eliminate them. Yes, there will be the other 95% of cases where children are bullied for other reasons, but at least the children can solve those themselves.

p.s. Will children be "narrow-minded and insecure because they can't wear what they want"? Please. :D What nonsense. A child must be psychologically stable enough just to attend school. So, whoever becomes narrow-minded because of such trivial things will have a hard time in life. Moreover, children can wear whatever they want after school.
Of course, many people don't like uniforms; that's normal. But to develop complexes because of this is an exaggeration.