I think you do need to go with the laws of the land when engaging in commerce. I think this law addresses the wrong end of the problem and blurring that line is what will destroy religious liberty.
The problem is a lack of privacy and a lack of decorum. It is wrong to push people beyond the addage that “if you can’t say something nice, don’t say anything at all”. This is a natural right which should probably be expanded upon from the concept of unlawful search and seizure to combat political correctness.
This law buys right into the fallacy instead of addressing a natural duty to not smear your bits all over public discourse.
It’s a band aid, not a fix all, and not touted as a fix all. But the brouhaha against it is quite illuminating as to the character of the source of the brouhaha.