Yeah there's already deadzones implemented (you can actually edit them on the menu), 360 controllers are a bitch for deadzones because of how the stick is loose in the centre. The problem in this case has been that people are turning at full speed to the right unless they steer in the opposite direction otherwise, what I believe it could be is something screwy with the input setting. The way the input works is that all the different possible inputs for both keyboards and controllers are named the same so the input can be read for everything in just one check, what's likely happening there is Unity is getting confused and returning the wrong value for the steering axis. I haven't seen many other Unity games that name axes for multiple input devices the same, so I would assume that is the likely cause.

The new input manager in that experimental build can only read either a controller or keyboard at any given time, not both. It will be interesting to see if that fixes the problem