To reiterate some other points: to my mind, citation (or not) is not about approval or endorsement, but simply acknowledgement of prior art. (I am in mathematics... in the the U.S., ...)
It is unfortunately true that most "peer-reviewed journal articles" are not at all scrupulous about acknowledging competitors' work. Nevertheless, if the question is about what one should do, one should acknowledge competitors, even if they've failed to reciprocate, and probably never will.
(Sadly-amazingly, a very good mathematician once told me that he scrupulously avoided looking at the papers of his competitors, so that he could in good conscience never cite them. One might think that he was joking, but, based on the citations in his papers, he was not.)
The issue of "non-canon" papers, e.g., arXiv and so on (for math, in the U.S., this is still slightly non-canon) I think is really the same, at least in the future. Sure, having editors approve and a referee or two approve is something positive... but, srsly, folks, if something serious of my own depends on it, I will want to have checked it through myself. For that matter, in recent years the requests for refereeing I get mostly say that it is not the referee's responsibility to certify correctness (!!!???!!!)... Whoa. Or, even if they do, that's only one other person... who very possibly has nothing on-the-line if the paper turns out to have a problem, in contrast to oneself, needing to depend on it.
That is, even before the internet and on-line archives, it was not truly feasible (or safe) to rely upon "refereed" journal articles. The main distinction between them and "preprints", in those days, was that people at universities did have access to the "published" (both literally and figuratively), but probably not to preprints, unless one had personal connections. This was why it was important in those days to go to conferences.
In particular, the alleged distinction between refereed and unrefereed (please, let's recover from burdening "published" with a special meaning so contrary to current reality) has become tenuous. Anything that is quasi-stably publicly available is "published", literally. If at a reputable site, by reputable authors, it is ordinarily taken seriously. Even if it is deeply flawed, it should be taken seriously, and acknowledged.
The subtler question is about language in one's own document to refer to other documents... that one may perceive as flawed, as pernicious, etc.