Gosh that’s an excellent question. It’s also very complex, and hence difficult to answer.
Usually I would not recommend Wiki, but the following article would appear from a casual reading to be Nihil Obstat for catechesis on Imprimaturs (but I have no authority to grant one, thankfully):
en.wikipedia.org/wiki/Imprimatur
I think bottom line, no individual censor is
infallible, except the Holy Father were he to make such a declaration ex cathedra on a particular matter, whether de fide (faith) or de moribus (morals). They are not instruments of the ordinary magisterium The authority of the Imprimatur is derived from the authority of the censor’s role. They can err. Please would someone correct me if I’m wrong.
For starters, the burden of proof should always be on the plaintiff. They must produce evidence supporting their claim that they’ve found contradictory statements in two books granted the declaration Imprimatur (let it be printed). If the statements pertain to faith and morals, one must deternine the degree of magisterial significance of the doctrine in question. My guess is they’d never get that far. But they could, in theory. And doubtless some censors have made mistakes. That does not invalidate either the doctrine in question nor the practice of scrutiny and appropriate censorship of Catholic documents.
One must always be aware that doctrines develop. On close inspection, most claimed contradictory propositions are actually reconcilable by examining them diachronically, that is, throughout the process of theological, historical development. OR they might just be contraries, in which case both claims could be true in some cases.