My "rule of thumb" (not related to poly) is that I limit discussion of romantic conflicts-to people who have already proven to be loyal to US and not JUST ME.
I don't discuss conflicts in my relationship with "friends" or family who are going to then judge my partner harshly.
In my poly dynamic-I talk freely with both guys about conflicts that arise because quite honestly-they tend to have good suggestions for me on how to deal with each other-even though they wouldn't identify themselves as "friends". Furthermore-neither is interested (NOW) in trying to replace or remove the other from our dynamic.
However-in the first few years, Maca DID want GG out of hte picture-so I did NOT share conflict info because it would have been giving him "ammo" so to speak.
Likewise-I don't discuss issues with my dad, he is a jerk about it. On the other hand, Maca's dad always has REALLY good advice. He adores all of us, wants to see ALL of us happy, safe, secure. So I know his suggestions are intended for the best interests of our FAMILY-not just me or Maca or whatever.
I wouldn't agree to a "no discussion" rule regarding our conflicts. Because honestly, I often need an outside perspective in order to figure out how to resolve things with myself-much less with my partners.
But, I would expect that I won't discuss conflicts with new partners-and my partners wouldn't either-until such time as the new partner has proven that they are fully capable of supporting US and not just "taking sides" with their lover.
Maca experienced the bad side of that-he vented and opened up about issues we were having to a new potential lover. Within a week or so she had "figured out" all of our problems (incorrectly) and decided I was bad for him and we needed to split. She spent a year trying to convince him to leave me (not for her-she had decided she wasn't interested in dating him). All based upon her perception of what he SAID while he was angry and hurt. To say it blew up terribly-would be putting it mildly.
The pain and suffering all of the way around was enough to convince him he doesn't want to even consider dating anyone else. It was hell.
So my advice to you is to try to find a middle ground. It's important to be able to talk, but things like that need to be privileges earned. With your girlfriend-maybe she could go to him herself and let him know that whatever you share regarding he and you isn't creating in her a desire to see him as "bad" or "wrong" or whatever. That she supports both of you in your relationship and ask how she can help him feel safer about you talking with her.
Sometimes, hearing those things FROM the person we fear to be judging us helps...
"Love As Thou Wilt"