[JLMounce]

Think about what is happening to the sway bar, which is rigidly mounted to the frame, when the axle articulates in motion comparatively to the frame. There is going to be some movement of the sway bar at it's connection to the axle.

Now that's not to say the rear bar isn't partly to cause for your new steering issue. You've added more rate to the springs back there when the axle isn't moving directly up and down. On hard acceleration, the pinion gear wants to climb the ring gear, which acts on the axle itself and tends to lift one side. This is why you see drag racers using air bags on one side in the rear.

This motion does transfer to the front of the car where any bump steer issue in the front can come in to play and cause what fwd drivers would call torque steer. The a body suspension does inherently have a good amount of bump steer in it and certain alignment setups can make that worse.