Judge Cogburn is, of course, an Obama appointee.
No, the FedGov cannot interfere with “the free practice thereof”. It does not matter if you wish to eat peyote in a kiva, worship Shiva in a temple, teach your kids about Jesus’s teachings in a school or celebrate Shabbat at your synagogue. The government has no say. Period. End of sentence.
This will get overturned. Private religious schools have broad exemption under the ministerial exemption. The US Supreme Court affirmed this just over a year ago.
https://en.wikipedia.org/wiki/Our_Lady_of_Guadalupe_School_v._Morrissey-Berru