This attempt to assert their rights will fail when it reaches the Supreme Court. Everybody knows it. Hobby Lobby will be fined out of existence. As for the Catholic Church, my bet is that they will find some way of complying wrapped up in many obfuscating words.
To throw this out at SCOTUS would require 5 justices to completely reject current evolution of First Amendment precedent, a total reset. It is remotely possible, but only because the Court *may* not be making its decisions independently, due to backchannel manipulation. However, even with that wildcard, the break with precedent would be so shattering it would throw the courts into chaos. Predictability of outcomes is the glue that keeps the system working even remotely well. Take that away, and its a judicial apocalypse. I don’t think its time yet for our would be overlords to try that. There are too many intermediate goals not yet met. And the justices will not go there willingly. If this were to be decided truly independently, Hobby Lobby would win 7 to 2, no problem.