Political theory is a branch of the theory of how to live. If God is our greatest good, then of course the truth about Him will make a difference to how to live.
When people say theology has nothing to do with political theory, what they usually mean is that either there is no God, or He is irrelevant to how we should live. But that is a theology; it is a doctrine about God. So such people think theology has something to do with political theory after all. The problem is that they insist we all live by their theology. And since they pretend that it isn’t a theology, they don’t think they have to explain what makes their theology true.
The claim is sometimes made that anyone who thinks God matters to how we live must want to bully people into obeying the true religion. But of course that depends on how God matters. If you believe as Muhammad did that God requires enforcement of Shari’a, then obedience to God requires coercing them to obey. But if you believe as St. Hilary of Poitiers did that “God does not want an unwilling obedience,” then obedience to God requires not coercing them, doesn’t it?
Tomorrow: What We Are For