Not sure I should answer this, because I am one of the more prolific posters, at least going by my post count total, which is somewhere in the top 20s or so for the entire forum. I wouldn't want to be ignored just for that, even if we don't appear to have met before in the previous 20 years.
If you're ignoring someone who started a thread, the entire thread will disappear from view. That's something that happened when we were still using vBulletin and it's also a thing with XenForo. So think carefully about putting that individual on ignore if they're the OP for any threads that matter to you.
Since they reply to threads and you're ignoring them, you're not reading their messages. Why this would result in "unread message" notifications, I'm not sure. That's not how it works in the Colosseum section of the forum, where I do most of my posting. Maybe the settings are different in the Civ section?
Or maybe it has to do with the method you're using to access the forums. I don't bother with using any part of my profile for this, because it's just extra work. If I want to see what's new in Off-Topic or Arts & Entertainment, I just go there and see if any threads have been updated. Of course I'll have received notifications for threads I'm subscribed to, or notifications of new threads. But that assumes that the OP or poster isn't on my ignore list. I don't get notifications for things posted by people on that list. I do get notifications about people I'm not ignoring replying in that thread. If you're subscribed to the threads that these people you're ignoring are posting in or being replied to, maybe unsubscribing would help. You'd have to remember to check those threads for new replies, but if the topic matters to you, that shouldn't be a problem (unless it's a thread that tends to fall off the front page and you'd have to search for it - but that's a chance you'd have to take).
If you want to not see any replies to this individual, you're going to have to also ignore the people who reply to them. It's inconvenient and can result in a cascade of putting people on ignore, but as far as I know, it's the only way to do it.
@The_J,
@leif erikson, is there a way to help the OP here?