In very very very broad strokes: truth deflationism is a theory of truth. A deflationary theory of truth says that to assert a proposition as true is just to assert the statement, and nothing more.
So, when someone says “‘the sky is blue’ is true”, they are just asserting the statement “the sky is blue”. This contrasts a more traditional theory of truth that states that propositions have a determine truth value that is independent of any thinker or speaker. I’ve seen deflationary theories of truth at play mostly in meta-ethics and epistemology. And probably metaphysics. (Epistemology being theories about knowledge)
Considering Catholic theology’s dependence on Truth (with a capital T), I’m going to guess truth deflationism isn’t compatible. At least in matters of theology. But I’m not a theologian so I can’t say for sure. I don’t think you have to be a deflationist about ALL truth so maybe it potentially can be compatible.
