How do I, or should I, bring up research that I did under someone who was fired for another reason?
From the tags, it seems you are an undergraduate. Therefore, I am assuming you don’t have a lot of other research experience to list. You also specify that the misconduct was not research-related. 

Based on these factors, I would suggest keeping this work on your resume/CV. I would stress the topic and content of the work rather than the person/group. Perhaps where you would normally list the faculty you worked under, you could list the university and department. Or you could perhaps list a post-doc who was a more direct supervisor, if applicable.

You are concerned about negative consequences of being affiliated with the professor in question. People don’t generally hold undergraduates responsible for professors’ conduct, so I think anyone who really considers the issue will not blame you. Personally, I would be more inclined to pity an undergrad in such a situation.