Is making non-culture-related exam questions culture-specific ever a good idea? So far I maintain the position that an exam question for a subject that is not related to culture should not be culture-specific. By that I mean a question should not contain any "jargon" only known mostly to the Americans. But I am not sure if it is just I am too cautious about such a topic that may possibly touch some discrimination issues.
Assuming that the class is not on American culture, you are essentially asking if it is ever a good idea to evaluate students on the basis of knowledge that was not taught in class and that they could not have any reasonable expectation of needing to know.

(Example: I wouldn't expect to need to know how american football scoring works when I went to sit an electronic engineering exam. At minimum, for a question that uses the setting of a score counting machine, someone who's watched football games in the past would need much less time to understand the prerequisites, and likely notice discrepancies in the machine's behaviour more easily. For fields like sociology, a cultural context might be unavoidable. In that case, the class should also contain this cultural context, so students can know what to expect.)

If your goal is to evaluate how well students have learned the class materials, then no. It is never a good idea.

If your goal is to measure how well-integrated they are into american culture, maybe? I'm not sure what kind of exam that would be, though.