"The Supreme Court now demands that religious people engage in conduct that seriously violates their beliefs."
Yes, so long as those beliefs are held in some sort of blind faith, instead of science...absolutely. You may not, in the name of your religion, deny a person the benefit of blood, organ, or tissue donation simply because you personally believe that such acts are ungodly or might transfer evil from one to another. Just because you pay monthly premiums, does not give you the right to decide what procedure(s) a doctor recommends or provides to another patient! Your beliefs have no standing in the halls of medicine and science.
Another point to consider is the origin of these beliefs...it is the Bible, specifically the Old Testament. Therein you'll find all sorts of laws and rules. Some of which to most might seem arcane, yet some still cling to them as though they were codified god-law. I mean if you like bacon, pork chops, ribs, shrimp, crab, lobster, or catfish, then stay out of the Old Testament! You aren't even allowed to cook your corn or potatoes with butter thereon?! And did you know that you are supposed to leave the corners of your field for the weird? I can assure you that any weirdos wandering the corners of fields through the Bible Belt would be shot on sight!
My point is that the Bible, or any other religious doctrine, isn't a cafeteria bar from the ancient past that you get to pick and choose which dish you will offend to non-believers with today. The Bible is for you to consume at your leisure, for you.
You have the right to do with your life as you please...that's it and no more. You don't need to personally agree with someone else's life choices to prepare them a hamburger, rent them a room, serve them pie at a counter, or bake them a wedding cake.
It is restrictive of interstate commerce to use your personal or religious biases to decide which patrons you will provide services you and won't. Imagine yourself, a pilgrim in an unholy land, unable to procure food, gas, or hotel services all because you openly prefer bacon-burgers and buttery popcorn?