One more time, religious freedom means you get to practice your religion, not force other people to follow yours. This isn’t complicated.
Imagine for a moment that [insert religion you don’t like] lobbies the government to force you to follow their rules on behavior, dress, etc. You see where this is going, right? Because you have imagined it. Now think for a minute, because it’s the same thing.
Religious freedom has to apply to everyone — including minority religions and those without religion — or it isn’t freedom, it’s favoritism.
You don’t like birth control? Don’t take it. But don’t block other people from taking it when you’re in a position of power over them.
That’s not you following your religion. That’s you forcing other people to follow your religion. And that infringes on their freedom.