Radial tires can have what I call ply steer. Something happens to the belts in the tires and one tire rolls with more resistance. You switched the tires and now the car pulls to the right. Yes, ply steer is the problem. I diagnosed my first case of ply steer in 1964 at a tire and alignment store I worked at.

Only different tires will fix the problem OR if the rear tires are OK put those on the front of the car.

Rotating tires doesn't cost anything if you do the work.