I don't think the accurate analogy is with mathematics itself.

Consider the belief that the universe must be fundamentally mathematical in nature, that if some aspect of it appears not to admit of mathematical description that's just because we don't understand it well enough yet, or our tools can't handle the complexity or somesuch, not because of any fundamental incompatibility.

That belief (to which I and probably most readers here subscribe) is an ideology as the term is being used here.

I will suggest that belief is to rationalism as mathematics is to rationality.