...but not in the way you intended.

If one wears a mandatory uniform, it will help with the integration an precisely avoid the religious issues!
Christians, jews and hindis wore exactly the same in my school.

If people are not allowed to wear items that are required by their religions, then the school is not facilitating integration. Only those with a more secular outlook will attend, or those with no other choice.

A few years later, a jewish school opened and half of the jews left our school for the new one.

And once a choice is offered, those who have felt constrained by the uniformitarianism will leave, thus inadvertently assuring that the remaining student body is even more homogenized.

I'm sure it's a fine school. So was mine. We had an open enrollment policy concerning members of other religions. In my years there, we had two Protestants -- they were Episcopal, referred to as "JV ["Junior Varsity"] Catholics" by an Episcopalian acquaintance of old -- and no members of any other religion. Uniformity makes things uniform, but not always in ways that are an advantage.

Regards--
Mary Anne
Mary Anne