There has never been much doubt about how a court would perceive these situations. The First Amendment is a Big Hammer compared to the concerns of a city policeman's ego (or even claimed national security interests, as evidenced in the Pentagon Papers case).
What I see here is police abuse of their authority, and then further abuse to cover up their tracks and claim "see, the system is working, we're investigating terrorists!" despite the fact that they don't have any real terrorists to investigate, and they know it. They have the resources to do it, while Tanya Ortega de Chamberlin is just one lone individual (who has now been deprived of her job as well) -- to fight this may cost many months and many thousands of dollars, while the worst punishment the cops will get is an admonition and the taxpayers will foot the bill for any fines.
recall the scene with Sir Bedevere in "Monthy Python," where the villagers dress up a girl as a witch just so they can have someone to burn, then rationalize the process? Well, the cops sure do look like those illiterate villagers from here.