With unmodified civics:
-Free Religion says "No state religion" on the civics screen
-As soon as you switch to Free Religion, you lose your state religion (the icon immediately dissapears from next to your name in the bottom right corner). I have never had another civ ask me to change my religion while I had Free Religion. On the religion screen, it simply says "Cannot convert to <foo>" even if you have that religion in your empire.
With two different mods I've tried:
-Free Religion says "No state religion" on the civics screen
-You keep your State religion. Other civs will ask you to convert to their religion. You have no difficulty switching between religions.
This looks to me like a bug, so I posted it here. I also posted it in the Creation & Customization forum, asking if anyone knew how to fix it.
-RdF