No one is impeding the person from his religion. What is being done is stopping the baker from attempting to enforce his religious beliefs upon others. You keep forgetting that he chose to enter into a business that serves the public.
the First Amendment does not protect BELIEFS. Read it carefully. It protects the FREE EXERCISE of those beliefs.
If a baker feels that he cannot, in good conscience, bake a cake for a specific wedding, then he is not abrogating anybody's rights. He is not forcing anybody to do anything against their beliefs. At most he is refusing to allow someone to force him to do something against his beliefs.
If his choice is...do the wedding or cease to do business with anybody, then that is forcing him to do the wedding; abrogating his religious rights.
That gay couple has a choice; they can get their cake elsewhere. Or not have one. Or make one themselves. It's the same choice I would have if I wanted a bakery to make a cake that is artistically repugnant to the owner, and he refuses out of sheer aesthetic disgust. THAT would be acceptable...
but refusing to bake a cake because doing so would violate his religious principles, a right guaranteed to him by the constitution?
I don't get this argument at all. It scares me, frankly.