I refer to Quietism in philosophy, not religion, and by Quietism in philosophy I refer to that view of certain philosophers that traditional issues of philosophy cannot or should not be the subject of debate or dispute, because they result from confusion due to imprecise or improper use of language, false assumptions, bad analogies, needless quests for absolute certainty. Wittgenstein, I suppose, was a great proponent of Quietism. J. L. Austin and Gilbert Ryle also come to mind. I think certain pragmatists were, as well.
It is a view I find seductive, or at least persuasive. Philosophers have been debating issues related to reality, knowledge, the good, the beautiful and propounding great systems regarding them for centuries, and it seems all for nought, and nothing is resolved; the same questions are still asked, and debated, and other, different, systems are propounded in what seems an endless profusion. Quietist (if there is such a word) philosophers have in many cases successfully (I think) demonstrated that much of this disputation and much of this grand systematizing is the result of confusion and imprecision in the use of language, or have otherwise pointed out that such questions as are being asked should not be asked, or are not really questions to begin with, and such problems as are being addressed by philosophers are not really problems.
I also question whether these traditional philosophical questions are worthy of further consideration. But then I find myself asking what would happen if they are no longer addressed by philosophers. If there is no philosophical pursuit of such questions (pursuit by philosophers, I mean) would this not leave the field open to those who are not philosophers? Philosophers at least endeavor to employ reason, and a method of analysis, to questions. Regardless of their success in answering them, should we not encourage the use of reason in the effort to answer the "great questions" rather than see them made the exclusive domain and concern of the mystical...the irrational?
Would that be the result of philosophy's abandonment of these issues, though? To the extent that people look to philosophers for anything these days when it comes to such questions, it seems they look to dead philosophers. This makes a kind of sense. It doesn't seem very likely that philosophers will come to conclusions regarding such questions that have not already been arrived at by the philosophers of the past (except, perhaps, the conclusions arrived at by the Quietists, and even those are of the past). Those who are mystics and are inclined to look to the irrational for answers to such questions probably will not even think to consider the work of living philosophers.
So, I don't think we need worry that most people will embrace the irrational in addressing the great, traditional philosophical questions, because of the efforts of the Quietists. But what of those who are not "most people"? What of philosophers themselves, or that amorphous class of people we call "intellectuals"?
There, I fear, the damage has already been done, in the sense that some philosophers, and many intellectuals, apparently have come to distrust and denigrate reason, and propound the irrational (e.g., postmodernists). This started, I think, in the late 19th century and extended into the 20th century and this anti-reason tendency carries on today, though it may be suffering a setback. Suggestively, this tendency is more or less contemporaneous with Quietism.
For good or ill, philosophers and intellectuals have a certain degree of influence. And by questioning reasoning, or science, as some of them have done, they make it difficult to combat those who make contend that answers may be given to questions and problems may be solved in a manner contrary to reason and science. To what end do we claim that certain religious views, or certain customs or beliefs, are unreasonable, or make no sense, if we insist and are on record saying there is no way of establishing, really, that is the case?
This is something that causes a legitimate concern. I'm not sure this is something which has resulted from Quietism, though. There is nothing in Quietism which encourages the denigration of reason as far as I can see. Reason is above all a method. Quietists may well contend that reason is not or should not be applied to the "great questions" because doing so is fruitless, but it doesn't follow from this that it is not usefully and beneficially applied to other questions and other problems.
Quietism doesn't require the abandonment of reason, then. It suggests only that it is misapplied in certain cases.