Where children are involved the Court often goes against the parents' religious preferences. For example, whereas an adult Christian Scientist can elect not to see a doctor or undergo surgery, where a child is involved the courts will step in. The Court did not allow polyogomy for Mormen men even though their religion at the time allowed it. I think it was a 5-4 Supreme Court case, but nonetheless the U.S. constitution did not offer the rabbo protection. There are cases now testing the rights of moslem prisonors to wear beards in jail, and every now and then the right of a Siek postal worker or cop to wear a turban on the job.
Bottom line is reasonable accomdodation.
But remeber too, reasonable accomodation goes both ways. A chaplin does not have to wear a kipa, he can wear an officers cap. During prohibition, kiddish is not limited to wine, but can also be said on grape juice, etc., etc. I don't know that I'm a mumche, but I know a fair amount about the issues. The short answer is that it's a very complicated question.