As a community driven site, this is a hard question. Questions are only supposed to make it on the HNQ list once it has received sufficient votes within a certain time span, and explicitly removing questions from the HNQ after they get on it I think goes against the community. This could exacerbate feelings that moderators are being biased against [insert group of people].
If we're worried that off-topic (but popular) questions make it on to the list, then we should close those questions. As Philipp points out in a comment, closing questions already removes them from the HNQ list. Similarly, if popular but badly worded titles make it on the list, the appropriate response should be to edit the question to make the title more appropriate since the list of questions is displayed network wide.
Quoting from the meta post:
In general, we recommend that you exclude questions that attract negative attention to your sites, that is, questions that are controversial, start large amounts of debate or arguments or even edit wars.
I personally don't feel this is applicable on this site, if a question gets out of hand in the comments then flags will be raised and moderators can lock the post and nuke the comments. I don't feel as some do that Politics.SE should shy away from topics that are controversial (so long as the questions are still at the very least on their face objectively answerable), since so many things in politics these days seem to be controversial. We would just be painting ourselves into an ever smaller box on topics the community as a whole allows.
There is some concern, especially on the subject of politics, that some questions may be upsetting to some users (for instance: this recently deleted meta question, seen here on archive.org for those without access).
I don't think there's much we can do about this, given that a question is asked in good faith and isn't being intentionally harmful in how it is constructed. To me it doesn't make much sense to implement a rule where any question about, say, "Communism" or "the Vietnam War" is intentionally excluded from the list of hot questions.
In summary: trust in the community itself and the HNQ algorithm as it is implemented at any given time, and rather than delete questions from the list modify borderline cases in order to make sure Politics.SE isn't intentionally triggering people when they're trying to solve programming problems.