Sure, Peterson and Vervaeke draw on cognitive science to promote some kind of religious attitude or spirituality. And indeed, on different grounds (social Darwinism/conservativism and Daoism), they say more specifically that we should submit to nature in certain respects. And it's that submission to nature that seems to clash with Catholicism. The Church burned witches alive for submitting to nature. So it's not about intelligent design, but about whether nature is a fallen, demonic place (as maintained also by the Gnostics and Neoplatonists).

Of course, many theologians have it both ways on this point since they think we can derive morality from "natural law." That's Peterson's move too. But it threatens Christianity with incoherence.