No, read the First Amendment. It is ONLY a prohibition on CONGRESS, not the states.
When will people realize that the feds are not their friend? You give the feds unconstitutional power like this and what happens next? The feds overturn state anti-abortion laws and force gay marriages on the states. They WILL take away your free exercise rights if you give them the chance. And letting them unconstitutionally enforce free exercise gives them that chance.
By way of circumstantial evidence, this tells a different story, it isn’t just Congress who has that limitation placed on them;
“Who’s Afraid of ‘Rocky Mountain Heist’?”
http://www.freerepublic.com/focus/f-news/3216319/posts