More importantly... you would be erecting a hurtle to equal treatment... something specifically disallowed. "
Worse premise. The idea of uniforms, while problematic, can't be invalidated on that basis alone. You're confusing the left's sacred cow of disparate impact with equal treatment under law. The type of confusion, in some quarters, that allows homeless people to defecate on streets with little consequence, because to forbid it might inconvenience them.
See Sowell's The Quest for Cosmic Justice for a thorough treatment of the idea. A very interesting read.