Wait, couldn't Christian Scientists use the same logic to actually claim absolutely no healthcare of any sort provided for employees at all?
Certainly possible by the direct logic here.
Basically the test;
1) Does the law create a substantial burden on their religious exercise?
Here, under the
Hobby Lobby standard, any requirement to provide healthcare that the organisation (limited to those controlled by a group of people with shared stated beliefs) professes a religious objection to would qualify as such.
If yes, go to 2. If no, law is upheld on this basis.
2) Does the law address a compelling state interest?
Here healthcare certainly passes. Although in
Hobby Lobby the status of contraceptive cover was never tested.
If yes, go to 3. If no law gets struck down.
3) Is the law narrowly tailored?
Basically, does it have too broad an effect or does it fail to address the primary goal. I don't believe this was a point of contention, although it could be.
If yes, go to 4. If no law gets struck down.
4) Does the law use the least restrictive means?
Boils down to whether the court can think of any method of achieving the compelling interest from 2 which would be considered less burdensome. It doesn't matter if the alternative method is practical or not.
This part of the test is what gives strict scrutiny its reputation as fatal to any law that goes up against it; you can almost always come up with some less restrictive hypothetical to eliminate laws you don't like. In reality it's not
all that bad, but still relies heavily on the preferences of judges.
In the
Hobby Lobby case the two alternatives were the non-profit exemption (itself subject to a challenge that looks likely to strike it down as still too burdensome under this same reasoning) or the government directly providing contraceptives.
If yes, law is upheld. If no, law is struck down.
A challenge to any healthcare by a valid religious group who bring a religious objection would fall down at stage 4 on the same basis. If the court views government provision of healthcare as less burdensome than an insurance mandate in the case of contraceptives I can't see how that's any less valid for wider healthcare. By that reasoning an American single payer, nationalised, universal healthcare system would be a less burdensome method in every case, so making any other system fail the test.