The FEDERAL courts have already stepped in on cases involving Constitutional religious liberties.
Which cases said that the federal government has the authority you claim it has with respect to state and local ordnances of the nature under discussion?
Since you haven't been able to point out anything in the U.S. Constitution that grants the federal government the authority you claim that is has nor are you arguing from a strict constructionist point of view, let me make this simple.
If the federal government were to be granted the authority you say it has; i.e. to explicitly step in and strike down a local ordinance like the one in Phoenix on the grounds that it violates the religious liberty of these shop owners, what's to stop a left wing activist point of view federal government from stepping in and creating a federal law that says in effect that NO private entity, anywhere in the United States can deny service based on sexual orientation (or any other criteria the feds deem appropriate) on the grounds that it violates the civil liberties of the patrons?
When you start coloring outside of the lines with respect to the EXPLICIT authority granted by the U.S. Constitution you start running into all these sorts of double edged swords, which is why we need more strict constructionism (Antonin Scalia) and less judicial activism (Ruth Ginsberg) rewriting the Constitution on the fly, along with much more push back from the States regarding asserting their rights.
The people of Arizona can address this egregious violation of religious liberty (by voting to Amend the State Constitution), it's exactly the sort of thing the 50 "laboratories of democracy" and the design of bifurcated separation of powers was put in place to do.