I think 忌口 could easily just mean “food restrictions” or “dietary restrictions”. Not sure if it’s a primarily-America thing, but in restaurants or even in conversation, “food restrictions” is pretty common. Like “你有没有忌口?” Unless there’s a nuance I’m missing.
I’ve always thought of 忌口 as Halal or Vegan and Vegetarian, but I think there are otherwords specifically for this: 清真 or 素食
I suspect a lot of words have nuance that can’t be described in a single word or chracter. The problem is that without external context, I find it really hard to know if my meaning of a word is corrrect. I’ve just been content with having a mild guess at the context, but I don’t know if there’s a way to double check word meanings, like a thesaurus perhaps?
I think HH uses official dictionary terms, which means that even an alternative meaning does exist it might not always show on the card (I’m thinking of something like the term “rubbish” here)