Edward Feser is a good example of this failure, writing:
The problem, in the view of many liberals, is that religious considerations are matters of faith, where "faith" connotes in their minds a kind of groundless commitment, a will to believe that for which there is no objective evidence. Opinions on matters of public policy, they would say, can only appropriately be arrived at via methods of argument assessable by all members of the political community, not by reference to the idiosyncratic and subjective feelings of a minority.
It's ironic that Feser complains about liberals who use straw man arguments against mixing religion and politics because, on a generous reading, the above is a massive straw man (a less generous reading would be that he probably knows better and, hence, is simply lying).
Why is this a straw man argument? Because what Feser describes isn't the argument against mixing religion and politics. Some people may occasionally say something like this, but it isn't the basic argument typically used in politicians and philosophers.
What is the real argument, the argument that Feser steadfastly ignores in his efforts to demonstrate that theism is rational? It's not that religious faith is "irrational" but, rather, that religious faith is "personal."
If you believe that the Bible provides answers to political questions, the problem isn't whether that is rational or not (there are plenty of non-religious ideologies that are irrational). The problem is the fact that this belief is based upon the private notion that the Bible is a "revelation" from God. The label "private" here doesn't mean "kept secret." It is better understood as contrasted with the subjects of political policy debates.
Thus, to say that religious faith doesn't belong in politics is to say that the status of the Bible (word of God? inspired by God?) and how to interpret it (literally? metaphorically?) should not become subjects of political debates or policy decisions. Other, secular philosophies can — but religious faith cannot.
This is why there is a "separation of church and state" but not, as Feser complains, a "separation of feminist theory and state." Philosophies like feminist theory can be debated in politics and the state can take sides in feminist theory. The status of the Bible cannot be debated in politics and the state cannot take sides in how the Bible should be interpreted. Such issues are subjects of private religious faith, not public reasoning.
This is the real reason why we should avoid mixing religion and politics. This is what Edward Feser studiously avoids addressing. Why do you suppose that is? Perhaps because he has no argument against it.
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