> the word cromulent ... is not even a real word
Only to a prescriptivist[1] trying to keep the language static. "Cromulent" is slowly making its way into descriptivist[1] dictionaries and is recognized about as often as any other new word, so it just as much a "real" word as other new words ("email", "google" (transitive verb), "truthiness").
> the correctness of using a singular they
The alternative is gendered pronouns which have several problems[2].
/* I'm not trying to nitpick your post; I just thought these two Tom Scott clips were fun and relevant to these grammar issues. */