How about we stand up for their religious liberty instead?
Cool. Shut down your hospital. Or rescind Ears' order.
They are the only ones in position to stop doing what they do when their rights or conscience are infringed. Same as you're the only one in position to do it for you.
I assume you don't control a large chunk of the nations hospitals. If they were to be abused to the point of shutting down in response, then that would send a large message. If the people are too stupid to understand the message, well, the people tend to get what they deserve.
And the people are usually very stupid.