I don't believe the professional and the personal can be completely separated. People can't stop being human and what does "personal" mean, at bottom, but that?
It's true that we shouldn't act on each other purely out of our own emotion but that's true personally too, not just professionally.
If you try to exclude emotion from human activity, including internet moderation, it ends up running the show anyways, just more crudely and unconsciously. Better to consciously give it a place—hopefully an appropriate place.
Questions like this have come up over the years and my sense (you may disagree of course) is that the community is happier with moderators who show feeling sometimes and can be related to personally. I could be wrong about that, but if so, it should have caused large problems long before now.