I have this problem and tried to fix this for one month, but to no avail. Basically when I squat downwards, the bar will drop to my left at the bottom of the squat, and the bar will remain slanted throughout the set. There is a feeling that my upper body is 'dipping' into the left hip more, resulting in the imbalance. The following are the observations I made after recording countless videos with different weights, technique adjustments, video speed, etc,
My right elbow is more flared compared to the left, and my hypothesis is that the left shoulder is not tight enough, resulting in dropping the bar to the left. Tried to fixed this by flaring the elbow out, pulling the bar down at the right. While this ensures the bar stay straighter, I still feel the dipping sensation in my left hip at the bottom.
Found out about lateral hip shift. My left hip flexors are extremely tight, and I might be shifting away from the left, resultingin bar dropping to the left. However I could not see the hip shift in my videos, or I just need additional pairs of eyes to help me out.
I have noticed that the tendency to drop the bar happens during sets with empty bar too. It just get worse in heavier sets. And after a lot of practices with my squats, my left hip flexor is even tighter than before.
I hope people here can help out. It is halting my whole progress. Thank you.