Well, um, that's uh...odd.
You may want to check to see if the traction control switch is plugged in, it's possible that it has come unplugged, which is why it won't disengage. If that's not the problem, I really don't know what to tell ya. I wouldn't think that the T/C would have much to do with the airbags, but then occasionally GM does some goofy things like that. I will say that you probably NEED the airbags more if you're driving around with the T/C off, especially if it's on wet pavement...but I doubt that GM had the foresight to see it that way.

Good Luck and welcome to the community.