Someone asked for an example of families who were not able to obtain religious exemptions even after going to court. Here is one from a couple of months ago. An Arkansas kid tried to get a religious exemption from the HBV vaccine requirement, but lost in court because the law restricted the exemption to members of "recognized churches".
The judge, Susan Webber Wright of Clinton sexual harassment fame, said that the law discriminated against individuals with sincerely held individual religious beliefs. The ruling doesn't really make much sense. The outcome was that the kid could not get the exemption.