At the moment, blacklisting a server is impossible on the new browser, and doing so on the legacy browser doesn't block them from the main one. This isn't something that's heavily needed, but it'd be nice in the future to be able to kick some servers you don't like off of the list so you don't end up potentially joining them by accident again in the future.
Worth noting, I am talking about personal blacklisting, before anyone starts getting mad. This is just a convenience feature from live that is currently missing from the game, that would be nice to have in the future whenever possible.