You're right
Now why anyone would take a job where the employer has that much control over their personal lives is what astounds me. Maybe we should go dancing around your hard drive and see if everyone is as immaculate as you're demanding your employees be? Come on, I respect religious rights, but I still think there's a point where you're imposing instead of just leading. You're the boss so your word is final. Too bad you didn't care a bit more about what others feel is their right.