Georgia

It sounds like a state version of the federal Religious Freedom Restoration Act.

As for your Jim Crow analogy, bear in mind that racially segregated lunch counters and so on were perfectly legal in many states until the federal Civil Rights Act of 1964. There is no constitutional right against discrimination by a private entity. There is no constitutional requirement that the federal government or any state government set about to uproot invidious discrimination by private entities.

If a state actually had a law on assault and battery that said, "You can't beat people up unless they're LGBT and you think God told you to hate them, then it's OK," that would raise an Equal Protection Clause issue. When it comes to bakers making cakes for same-sex weddings, though, the Constitution is silent. Would-be celebrants must rely on statutes to protect their rights.