A one level difference is negligible. You can reach level 31 through Crucible and Faction gear so there is no reason to be up in arms about anything.
It's your own fault that you are still at 29 with Rare gear on. Purchase the armor required for 31 and you'll be fine.
I agree that this game is heavily weighted towards the PvE side, however just playing one part of the game will lead to you being left behind. If I only did patrols, I would have nothing to show for it (Potentially. I don't have the best of luck). If I participate in every aspect of the game, I'll be able to enjoy the rewards that come with that.
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I am a 31 I was just wearing un leveled PvP gear. Blue chest is because my other chest is exotic and I'm using exotic helm. Legendary chest usual just ammo.
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Then you'll be fine. There is really no difference between the level 32 and 31 players in IB. Wait and see. Being max light level is really only a thing that is required for the raid. In Crucible, and even IB, it doesn't make a big difference. The only time it makes a huge difference is if there is more than a 3 level gap (if I remember right). At level 31, you should be smashing the faces of level 28's.