So, I'm playing Ultima V, and I was wondering: can you help the Resistance, join them and still get the Balck Badge from the Oppression to get through Blackthorn's castle?
Does your karma get penalized for this duplicity?

I love this game and I'm trying to get the most out of it, so I'm trying to do everything and to get as many clues as possible from NPCs.

Yeah you can join both the resistance and oppression. Joining the oppression gives you a certain item that makes part of the game easier but you don't need to do it.

though it may take a little bit of digging, this 'walkthrough' has the most comprehensive explanation i've seen for why to bother (or not bother) with the Oppression: http://lparchive.org/Ultima-4-5-and-6/Update%2027/
chief among the criteria is that several instances in which you'd expect Karma to be penalized, it apparently isn't; also, 'legitimately' acquiring the Oppression's password requires a fairly ugly decision (which doesn't appear to hurt Karma either, but while i have called the 'join-the-Oppression-or-don't' part of the link somewhat comprehensive, i don't consider the author a solid authority by any means (based on a variety of "i have no idea why ____" remarks scattered throughout the 'walkthrough').

Just fly on the magic carpet through Blackthorn's Castle, and you won't have to worry about traps or those gargoyles attacking you when you go to grab the crown (it is the crown that is there, right?).