Quine thought (I gather) that revising our logic is not an option (is illogical) because to do so would be to make too many changes throughout our web of beliefs; but we might expect inferences made automatically (unconsciously) to change as readily as our natures (as we grow up, and fall under new hormones, or take on new roles, or as we grow old and lose some neurones, and so forth)—an upsetting but not untypical thing for brains to do—and inferences made more rationally (consciously) had already changed enormously by Quine's time (set-theoretical proofs having replaced Euclidean intuitions) without massive upset to most mathematics, or to the scientific method. There were huge changes to our physical (and social) world-views, of course, and there must be some ordering to our rational revisioning; but what?
......I suspect that, really, we still reason according to the Euclidean intuitions that still structure the (paradigmatically) real world around us; that we don't actually have a choice about that. Consequently we can revise our theoretical logics (e.g. adopt a quantum logic for physics, if that's easier for the physicists) without that affecting many of our scientific beliefs; although lots of people therefore have a rational distrust of modern science, because it seems (when viewed by the natural light of our common sense) quite illogical beyond its technological applications.