I know one must not cross-post between SE sites. But am I allowed to post the same question, say, on AskDifferent and Apple Support Communities?
There is nothing stopping you. But if you receive "the" answer on one of those other sites then you could also either post the answer here, encourage the answerer to post it here themselves, or write an answer yourself that references and summarizes the answer you received elsewhere.
Essentially, if you post a question here then you should endevor to have an answer for it here too - otherwise there is no point posting it here to begin with.