I also think Steel Wind has it right, it's fundamentally a player issue, not a rules or alignment issue, and needs to be resolved with the other players.
That said, the underlying CHARACTER actions are interesting. I agree with those who say that the barbarian's theft constitutes a CHAOTIC NEUTRAL act rather than an evil act, but I don't understand why the DM would threaten your character with ANY alignment shift due to retaliation. Even if your actions were not fully justified, as a LN character, if you could justify your actions in terms of some principle of absolute law, it would be consistent with your alignment.
I've had similar player vs. player experiences as a gamer, specifically when a CN gnome rogue played exactly the same kind of trick on me in a game and then justified it on the basis of "playing his alignment." Things escalated and I attacked him (in-character). The DM allowed this as a role-playing experience which developed both of our characters and ultimately the other players, also RP-ing deescalated the conflict with no bloodshed. It provided a memorable gaming experience for all of us, even though the player was being jerk-faced about it. And it all worked out for the best.
Then again, we were all very experienced gamers in our 30s, 40s, and 50s. If we had been teenagers, I'm not sure things would have worked out so well.