Never having studied philosophy, I have a seat-of-the-pants definition of empiricism: It’s the process of deriving truths from observed phenomena.
Religion is by definition non-empirical. That is, religion starts with the idea that certain things (notably the existence of “God”) are known to be true even though they can never be observed.
The reason why religion has no place in government is because public policy should always be based on empiricism — that is, on a close observation of what actually works and what doesn’t, rather than on faith.
But empiricism isn’t enough. A government could be founded entirely on empirical principles and yet could be vicious and brutal. Effective governance, it seems to me, rests on the twin pillars of empiricism and compassion.
To the extent that religion counsels compassion, it can be an effective advisor to government. To the extent that religion counsels intolerance of any kind, it should be barred from participation in governance.
If you want to practice intolerance within your own church, go right ahead. (Whether you have the right to teach intolerance to children … we’ll talk about that some other time.) But if you expect the government to enforce your intolerance using police and the courts, your religion is an enemy of freedom.