There are two very good reasons to separate church and state. (Don't let history alone decide. We can think for ourselves too.)
1) So public policy is not solely defined by the superstition of mythos. (I know all you believers believe its real. But, until Jesus makes his encore, God not liking something isn't going to help anybody.)
2) Here's the big one. Whoever came up with it probably had the best intentions... But to set authority on a celestial plain does not make all men equal. It instead allows those arrogant enough to claim connection to that authority a chance to become emperors to the religion's believers. They play off imagined fear and imagined hope, using it to steal their way into important decision making positions.
And, unfortunately, those willing enough to take that low road don't have much else to offer. Thus, they end up making a mess of the world.
The Bible is utilized to justify a lot of nonsense. So's the Qur'an... Both, especially in the regard of modern issues, leave much to the imagination. Quite honestly, the symbolism can often be so vague that you can get them to say anything.
Take the "ass of men" tale.
Which, I assume, is based off the story of Ham. Noah became drunk and naked and Ham bragged about it to his brothers. Noah hence cursed Ham (the Canaanites anyway) for allowing him to be seen naked. GENESIS 9:20
How many racists have used Noah's "ass of men" story to vilify any ethnicity of their choosing?