If it's a private organization, then, depending on state/local regulations, this would be legal. Pretty sure that since she's on government payroll, they can't fire her for stating her personal beliefs off the clock. And technically, it's not forfeiting her right to free speech if she's only getting fired. It would be if she was getting fined or imprisoned because of it, but until it's a legal repercussion, then it's not a violation of free speech.