It really depends on what you're using citations for. Peer-reviewed papers don't necessarily need a transitive property where they only cite other peer-reviewed

It really depends on what you're using citations for. Peer-reviewed papers don't necessarily need a transitive property where they only cite other peer-reviewed papers (which only cite... etc.). Norms vary by field, but in most fields, it's always been acceptable to cite various kinds of non-peer-reviewed literature, such as technical reports. Even popular press articles or blogs are fine, as long as they're cited appropriately, not to back up critical claims. Ultimately the single paper under review is peer-reviewed for whether it demonstrates its own claims, and that depends in part on the reviewers judging whether it uses citations appropriately, meaning that it can cite anything it wants, as long as it doesn't cite things to demonstrate claims that the citation can't really support. In mathematics my impression is that citing arXiv papers is usually done appropriately. If a surprising proof of a longstanding open problem was recently posted on arXiv, people won't usually cite it as authoritative right away. Instead a citation will be worded with something like "a recent claimed proof by so-and-so...", making it clear that it's still preliminary and not to be treated as a sure thing yet (how strongly to add this caveat is a bit of a judgment call). As a reviewer that's usually what I look for. If someone cites an arXiv paper (or tech report, or even blog post) to give context, to credit other teams who are doing related work, to point out alternative approaches that the current paper isn't investigating, etc., that's perfectly fine. Those are more like informational "see also" citations. If a paper cites an arXiv preprint as authoritative evidence of something that is really critical to the current paper itself being correct, then yes, that's where it can be more iffy and I'd ask the authors to either qualify that claim more, or bolster it with another more solid citation. There is a little bit of a problem with this currently in machine learning, where some people make overly bold/general claims in arXiv preprints that their methodology/data can't really support, and other people sometimes cite these claims a bit too credulously. Important to push back on, but not to the extent of banning arXiv citations.