The last time I checked, no one in the U.S. is being punished for what they believe or for expressing that belief. So what's the fuss about? It's not a concern that people can't express their own beliefs. No, it seems to be a concern that people will not have the license to impose their beliefs on others.
I suppose it shouldn't really have come as a surprise. But there it was in black and white in a recent court document: Trinity Health, one of the largest health care systems, saying that because of religious exemption laws, its Catholic affiliation allows it to violate the law and refuse to provide pregnant women with emergency medical care.