It seems like such a simple argument, and some may allege that it's simplistic, but here goes nothing:
1. There are immutable truths of logic, mathematics, and ethics. (Premise)
2. If Naturalism is true, everything is mutable. (Definition)
3. Therefore, Naturalism is false. (From 1 and 2)
Given that Naturalism is false, theism becomes a much more viable option. (1) may be demonstrated transcendentally, e.g. the rejection of the laws of logic is self-defeating. The reason (2) is correct is because Naturalism, at least on most accounts I'm familiar with, states that every existing thing is physical. Since all physical things are capable of change, it follows that every existing thing is capable of change (mutability).
Of course, the philosophically sophisticated Naturalist might amend such a view. Let's call the former Naturalism-A and the latter Naturalism-B. She might hold, like Bertrand Russell (incidentally, should Russell be considered a Naturalist?), that there are objective, immutable truths of logic, and so forth. The central thesis of Naturalism-B, then, would be this: there are immutable truths, but all concrete particulars are mutable. Immutable truths exist in a kind of Platonic realm.
Naturalism-B is probably more tenable than Naturalism-A, but does Naturalism-B survive philosophical muster? The problem that Russell, Quine, and other Platonists faced in the past, and what remains a major difficulty today, is Plato's "third man" argument. If there are immutable truths, why do we, mutable minds, have knowledge of them? I've defended the causal objection to Platonism in the past, and it seems equally relevant to Naturalism-B for as long as Naturalism-B is dependent on Platonism or something close to it.