Well if one wanted to be precise, one would point out that the US legislation (Federal) was signed by Clinton ...
That federal RFRA, and many of the state ones that follow it, are somewhat different from what the Indiana and Arkansas legislatures originally proposed, though the changes that both governors are seeking may bring them more or less in line with the federal model. One difference is that federal legislation aims at protecting what I call "consensual religious activities" against government interference, like allowing religiously required use of wine or peyote regardless of any prohibitionist laws. So, activities where the only people affected are the ones claiming a religious obligation, as opposed to claiming a religious obligation to not serve certain customers while providing the same service to others.
If I'm ever in charge of organizing a bachelor party, I'm going to find me a Muslim restaurant and demand that they cater the event, complete with strippers and booze.
None of these laws touch that case, since such a restaurant would not offer such a service to anyone: the debate is about whether a business that routinely offers a service can then decline to offer that same service to certain customers. For example, if a restaurant is open to the public, but the owners claim a religiously based prohibition on associating with people of certain races or people of certain other religions, are they allowed to refuse service to such people?
P. S. I would rather that the original "Religious Freedom Restoration Act" has instead been a "Personal Freedom Restoration Act", because the acts it is intended to protect (ones that only affect wiling participants) are better off being protected without any need for a tie to religion.