A state school cannot impose consequences that violate a student’s free speech rights, even if it has a code of conduct, and even if the student signs it. To put this another way, a state school cannot enforce rules that conflict with the U.S. Constitution. It might be the case that the ROTC program can restrict speech rights more than a state university, though.
A couple of other points here (I’m feeling contrary today). While I think this was almost certainly a racist act, are “ghost costumes” like Charlie Brown used to wear now inherently racist? Is it OK to have a sheet with two eyeholes, but not a pillowcase (because that’s too much like a hood)?
Finally:
Many Christians (I don’t know about most) believe that only people with specific beliefs will go to heaven, and that everybody else (including Jews, atheists, Buddhists, Muslims, and other Christians with the wrong beliefs) will go to hell. I suppose one could call this bigotry, but complaints about exclusiveness in religion seem odd to me when expressed from a Jewish perspective.