I'm having the same issue with bf1, moving to the right as well. It's very noticeable when in a tank.
I have another controller that doesn't have this problem, but it's very used and the stick is too soft, specially when I move it up.
I might get a new controller today, but it's looks like it could have the problem too or have it with relatively little use. I'll let you guys now if it works.
Just curious, did you get a new controller?