It should be clear that I am almost a medieval scholastic in my the-ology. I have no time personally for open theism or process theology. However, I would make a big distinction between the two.
1. Open theism, as I define it, is the idea that while God is omniscient and God is omnipotent and God is distinct from the world, he has of his own will decided not to know the future so that we can have free will. This is an Arminian twist and it is a conservative twist on normal theology.
It is an Arminian response to an argument I consider silly. A certain Calvinist says, "If God knows the future, we cannot have free will." The open theist (in my mind) responds, "What if God chooses not to know the future so that we can be free?"
Remember, I am a medieval scholastic who thinks God sees all time in an eternal present. "You are both silly," says I.
It is conservative because it more or less takes the Old Testament literally. "Where are you Adam?" Poetry, says I. "God chose not to know where Adam was," says the open theist. "Silliness," says I.
I don't think Wesleyan-Arminians should worry much about open theism, even if I think it's silly.
2. Process theology is something quite different. Process theology does not believe that God created matter and does not see it as under his control. Sometimes, process theology sees God's nature and character as something that is in a process of change along with the universe.
Let's be clear. Wesleyans believe that God does not choose to direct everything that happens in the world. But Wesleyans believe that God is in control of the universe.
Wesleyans believe that God chooses influence over determination, but process theology usually holds that God cannot determine. That he can only influence.
A Wesleyan can easily believe that God created using evolution, but a process theologian believes that evolution is/was not under God's control or supervision. Indeed, a process thinker believes that God himself is evolving in some ways.
3. So there you have it. Schenck's perspective on these things. Open theism is silly but generally harmless. I would not support a Wesleyan college or university hiring a process theologian.