I've suggested an edit that "fixes" the post (so if the edit is accepted people should look in the history to see the original form). That said, the intuition of the change I made is that the backslashes needed to be escaped. However, they probably shouldn't need to be escaped and so some MathJax or Markdown reconfiguration may be needed. (At which point my suggested edit will likely need to be undone.)

A problem that is almost certainly related is that sometimes the Markdown processor will convert substrings delimited by underscores to italics when those underscores are part of the MathJax, thereby breaking the MathJax. Peter Taylor's issue and this one are almost certainly due to the Markdown processor not being aware of TeX dollar signs. This leads to the Markdown processor breaking the TeX. (I deal with a similar issue with my blog.)

@Derek, now that you mention it, I'd noticed that I had to escape the backslashes for backslash-curlybrace to get the multiset notation to work. I should have put 2 and 2 together myself. Thanks for the diagnosis.

Note to site admins: I haven't wrapped the multiline stuff in $$ because it was rendering identically in the preview. IMO it would be a perfectly reasonable approach to look for/write a Markdown plugin to treat the MathJax delimiters $ and $$ as start and end delimiters of a section where escapes should be ignored, and I would be happy to add some $$ to my answer.

Related: https://math.codidact.com/questions/278763