I help run a popular online writers' group. Would it be inappropriate to talk about this in an interview, seeing as the group is online? For example, if I'm asked "when as a time you disagreed with a colleague?" could I refer to a situation where I and someone else who was in charge had a conflict in this group?
I don't think there's an issue with appropriateness, but there may be an issue with relevance.
If you're managing a remote team, it's obviously relevant. If you're managing people face-to-face, the only opinion on this that will matter is that of the interviewer.
The skills in managing remote and local teams overlap, but aren't identical. Given a choice between online and offline conflict resolution, I imagine most people would pick offline if the job is face-to-face.
If you do go with the online example, I'd be prepared to give an offline example as well.