It's your router that flips out because it can't handle the amount of incoming connections (each server). I have had the same experience before with refreshing server lists on steam or when using torrents with alot of connections and it got fixed when I got a new router.
It's not really a bug, but facepunch should not force you to refresh all the server if all you want to do is look/refresh your history or friends tab. Either get a new router or connect through the console (F1)
So it's normal for them to hit 100's of ports? I don't think so.