In Employment Division v. Smith (1990), Conservative icon Antonin Scalia, argued that a person may not defy neutral laws of general applicability, such as public accommodation laws, as an expression of religious belief.
"To permit this would make the professed doctrines of religious belief superior to the law of the land, and in effect to permit every citizen to become a law unto himself", wrote Scalia.
The Sweet Cakes by Melissa case, the Oregon bakers who refused to bake a cake for a gay couple, is a perfect example of what Scalia was talking about.
The Oregon State Constitution makes sexual orientation-based discrimination in the State illegal. It is a duly-enacted law, existing within the powers of the State legislature to enact.
So if you run a business in Oregon, the State's laws and codes do not allow you to refuse service to anyone based on (among other reasons) their sexual orientation.
As US citizens the US Constitution, the Supreme Law of the Land, does guarantee our religious freedoms, but the case of the bakers is not truly about religious freedom, but rather about whether or not one's religious beliefs can allow a business owner to conduct a business (not a constitutionally-protected right, but a licensed and regulated activity) in direct violation of State laws and regulations.
Someone said that they wished that they had a "go to another cake shop to get your cake" guy, when in fact the real answer would seem to be to either not make the choice to run and operate a business in a State where the State laws may be in conflict with your religious beliefs, or to simply not bake wedding cakes, if you are a religious baker running a bakery in a State that (lawfully) does not allow businesses to deny services based on sexual orientation.
The general principle here is Federalism.
The State of Oregon, and the citizens of that State, are supportive of that clause in their Constitution, and the US Constitution does not prohibit the State the right to enact that law (Amendment X), so representing the Sweet Cakes by Melissa case as one of religious liberty is wrong.
The bakers can believe, worship and live all in accordance to their religious beliefs, as protected by the First Amendment of the Constitution.
A constitutionally-protected right to run a business however, does not exist.