There is a huge difference between child says they want to wear something different and mum doesn't want them to wear the standard uniform because "it doesn't look nice". The Op here is the latter one.
One you can give them guidance and if they want to continue they cope with the consequences and either decide what they want to wear is their choice, or decide to follow the others. It's a good lesson.
I used to hate being different as a child. Dm knitted me a lovely warm cardy which was, looking back, absolutely gorgeous. I wanted those cheap polyester cardies that everyone else had. No matter how many times dm told me (and other parents too) how lovely my cardy was, I coveted quietly those polyester ones, so I could be the same as everyone. I never told dm that, because I knew she'd spent ages knitting it, but all I wanted to be was the same. Yes, I was probably warmer, and more comfortable, but that wasn't the thing that mattered to me at that age.
Ds announced when going into the juniors that he was going to wear summer dress because it was the only way to avoid wearing a tie. I said fine as long as he was happy being the only boy wearing it. We had summer dresses (he's got big sisters) but the suggestion never came up again. At that age he didn't like being different.
At secondary school he was frequently the only boy in the school in shorts, and certainly by year 9 - 11 was the oldest boy in shorts, but by that age he felt being comfortable was more important than being the same, and was capable of giving a (fairly witty normally) response to anyone who commented. He was even called "Shorty" for a length of time, and he wasn't sure if it was a reference to his height (he grew late) or wearing shorts but he wasn't bothered.
The difference was that he chose what he wanted to wear with the knowledge that he would be different if he went with what he was comfortable with.