[technicaldonut]

I think this depends on how full the plane is.

Moving a few people probably doesn't cause an issue if the rest of the plane is completely empty.

If you move 20 people from the right side to the left side of the plane this will probably have some kind of effect.

On smaller regional aircraft they sometimes ask people to move seats to the other side or back to front.

[bdamm]

Moving people left and right has absolutely zero effect on the controlability of the plane, because the ailerons can compensate for much larger movements than that. What it might have an effect on, though, is the overall efficiency with which the plane flies. It is more efficient to have the center of lift and the center of gravity matched, than not.