First of all this is not a liberal democracy. This is a constitutional republic. And people are certainly free to not work for any group that does not provide the health care options that they want. Just because a strip club might provide great insurance benefits, doesn’t mean that I want to work there. It’s my call. By saying that some people have to give up rights guaranteed by our Constitution, you are in effect saying that rights should only be guaranteed to those you agree with.
You wouldn’t like it if someone told you that based on their laws, you would have to wear a burhka would you? Wouldn’t that offend your first amendment rights? This administration has consistently violated Constitutional law, but because it is something you agree with personally, it’s ok.