You can't teach respect for difference or for diversity in an environment where children are forced to all conform to uniform policies.
"We should all respect each other and accept difference..."
...can never sit well with:
"You will be publicly called out for divergences from the norm."
I am in the US and my DCs attend /have attended a non uniform high school, which is the norm in the US. The school catchment has a huge income range. (It's neither here nor there, but the winter weather warrants seriously warm outerwear).
No specific brands have ever been banned or ever will be.
The reason for this is that nobody gives a hoot what anyone wears since the vast majority of the kids have been wearing their own choice of clothing from their first day in school at age 4 or 5.
Children are not 'bullied for not having the right label'.
They are bullied because there is something seriously wrong with the bullies - their home life, their relationships with parents and their relationships with themselves. They are bullied because the bullies have no self esteem and are aggressive and live in a dog eat dog culture.
Tackle the bullies, not the random thing they choose to wield against other children.
Tackle the culture of envy.
Tackle the conformity culture in schools.