It would violate the 1st amemdment to prevent that. Freedom of religion.
If someone would say, "But you don't have to wear your cross to be a Christian", then you must be equally be okay with forcing an Orthodox Jewish man to shave off his facial hair, because he doesn't have to wear facial hair to be Jewish, according to some people's interpretation. Forcing either one would be coercive and wrong. Wearing my badge of faith is part of my witness to my faith in Christ, and the government cannot legally force me to remove it.
Btw, my state actually passed a law to specifically allow teachers to say "Merry Christmas", or whatever holiday wishes are appropriate to their faith. It's ridiculous that they even need a law for that, but I'm glad it's there as a protecton. I'm a teacher, not a robot.