Compelling state interest.
It's what gives the state the power to legislate against a host of issues. i.e. prostitution, gambling, adultery, drug use, public intoxication, etc. While indiviual acts in and of themselves may have a debateable or negligible impact on society if permitted wholesale society itself becomes untenable. Nothing in the Catholic teachings about BC or not funding is going to destroy society. On the contrary the sexual revolution has had demonstrably ill effects on our society (DISCLAIMER: m r fornuhkater).
I call compelling state interest, "The Idiot Sanction." Yeah, you're gonna do it but if you're mindful enough to keep it out of sight of the authorities you're probably exercising enough discretion to not ripple the world of those around you. However, if you do get caught than society has the right to impose "The Idiot Sanction" because if everybody acted as dumb as you then the number of fatherless children, drug addicts and stoned layabouts would be too great to allow for a functioning society. Moral anarchy ALWAYS leads to social anarchy. Every time. 100% surety. Guaranteed results. It's as much a law of nature as the laws of thermodynamics.
Now as far as the COTUS is concerned Obama has undoubtedly attacked not only the Catholics but the very COTUS he is sworn to defend.
The argument need not proceed any further. It's as malicious as it is unconstitutional. To engage in debates of whether or not Catholics are superstitous is to make our rights contingent upon matters of practicality. They are not, nor can they ever be; otherwise they cease to be rights.
The law is the law is the law and the COTUS is the law that governs the lawmakers...not the people.
Your example needs a little work...
Be that as it may, at one time the LDS church did endorse multiple wives (dumb asses!) and the government did outlaw the practice in direct confrontation to those teachings. If the muzzies ever tried to play that shit here (dumb asses!) the state still has a compelling interest to say, "I don't."