How Christians of differing theological persuasion reconcile free will with God's sovereignty

There are two different views of what free will is. One is called libertarian free will. The other is called compatibilist free will.

Libertarian free will is the view held by most Christians. There are different approaches to solving the problem of free will and God's sovereignty.

One is called open theism. This is the view that God's plan for the future is not exhaustive. In fact, he doesn't even know the future exhaustively because he can't predict what free creatures will do with perfect accuracy. While a lot of Christians will accuse open theists of denying God's omniscience, open theists disagree. In their view, to be omniscient is to know all true propositions, but they believe there is no truth value to future tensed propositions about free will actions. Since there isn't anything for God to know when it comes to your future free will decisions, the fact that God doesn't know what you will do tomorrow doesn't count against his omniscience.

Another solution is called Molinism. According to Molinism, before God creates anything, he knows what each possible free creature will do in any possible set of circumstances that creature could ever be in. With that being the case, God considers all the possible outcomes that would inevitably happen if he decided to create the world in a certain way. So eventually when God does decide to create the world, he takes his knowledge of what people would do in whatever circumstances into account. So the free actions people take become part of his plan. He incorporates those actions into his plan and works with them.

Another solution is to say that God exists outside of time and is able to observe the whole spectrum of time and everything within it. But within time, we have free will. In this view, the direction of entailment is what allows us to be free. It isn't God's knowledge that entails that we choose in particular ways; rather, it's the ways we choose to behave that entail what God knows. So our free choices determine what God knows; what God knows does not determine our choices. So our choices can still be free.

Compatibilist free will is different than libertarian free will. Libertarian free will is the idea that when you act freely, there are no antecedent conditions prior to and up to the moment of choice that are sufficient to determine what that choice will be. That includes a person's own mental states, such as their desire, motives, preferences, inclinations, etc.

Compatibilist free will is the idea that your choices are free to the degree that they follow from your own desires, motives, preferences, inclinations, etc. You're free in the sense that you're doing what you want to be doing. So in this view, your choices are determined by your antecedent mental states. Your mental states may, in turn, be determined by something else, including your environment and God himself. Since this is a form of determinism, it's perfectly consistent with God having an exhaustive and sovereign plan.