First of all it seems to me that you are of the opinion that logic is the only means by which a human should act, which itself is very inhuman, particularly since you seem to have your own assumed criteria of truth and likely also are an individual who makes the assumption that the world is purely physical (my personal speculation), which has absolutely no logical basis - it is an a priori assumption which all of your "logic" (utilizing your criteria of truth) is centered around. The same goes for assumptions that it is not purely physical - they are at their core "beliefs" (but we can still call them assumptions if that makes certain people feel better) and have no truly logical basis...They seem subjectively self-evident.
Second, I think nearly everyone cares about logic (otherwise they would not fear things like falling, pain, and similar acts of causality), however,
they do not base their use of logic on the same criteria of truth as you, nor do they, perhaps, make the same assumptions you do about the
fundamentals of the universe (some are physicalists, some idealists, and some others are panpsychists).
The basic system of logic is a universal system, but there are at least three major branches in it which form vastly different worldviews and even
further differences if one happens to give say...the criterion of subjective emotional feeling a higher priority within their own use of logic than
The rules of logic have no ability to distinguish truth by themselves, that is up to the individual and their personal criteria of truth. So you have
to excuse me when I am given the impression that when you say "some people don't care about logic" what you are really saying is "Some people
don't care about my personal use of logic and my personal conclusions (based on my theory of truth), and I am flabbergasted as to why they do not
think more like me?"