In third person this is most likely due to the camera angle as the camera is over the right shoulder. Upload a video of first person view from either patrol or crucible so we can see if there is a problem.
It can also be your joystick is starting to wear out. Uneven wear on the sensors is common as you will inevitably be using one direction more than others.
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Uploading now, will post that and comparison video with borderlands where there is no issue