Is it illegal to take away Constitutional Rights?

I go to a Catholic school and the rules there have me questioning if these rules are legal. Here are some examples: they won't let us grow hair out past our collars/eyebrows; they don't let us wear normal clothes, we have to wear uniforms; on out-of-uniform days, we can't wear certain things; we need our shirts tucked in. This school is a private school. Since it's private, can they actually tell us to do these things, or can we actually protest these rules because we don't have our Constitutional Rights?