Before there was Process Theology, there was Pragmatism. Elaborating on the subject in his lectures and book (of the same name) in 1908, William James explained why he believed we badly need a middle way between empiricism, "going by facts", and rationalism, "going by principles."
As James noted, most of us want both science and religion. Here's how he explained what Pragmatism means.
"The pragmatic method is primarily a method of settling metaphysical disputes that otherwise might be interminable. Is the world one or many? Fated or free? Material or spiritual?
Here are notions either of which may or may not hold good for the world; and disputes over such notions are unending.
The pragmatic method in such cases is to try to interpret each notion by tracing its respective practical consequences. What difference would it practically make to anyone if this notion or that notion were true?
If no practical difference whatever can be traced, then the alternatives mean practically the same thing, and the dispute is idle. Whenever a dispute is serious, we ought to be able to show some practical difference that must follow from one side or the other's being right."