This is exactly the issue at hand today:
The fact that a cabinet secretary can, of his or her own volition, without an act of Congress and with no practical avenue of redress, issue regulations mandating that someone must do something that he or she as a matter of personal ethics or faith would otherwise never do, is an assault on the country’s very foundation.
This isn’t an abortion issue, this isn’t a contraception issue, this isn’t even a moral issue. This is about the government not being able to force individuals and organizations to violate their own conscience.
The fact that anyone would support this is baffling, and stands against everything that still makes the United States a great place to live. Taking away constitutional rights is a slippery slope.