kvmz

During normal driving I can hear a purring/grinding noise while in motion. It gets faster during acceleration and slower during deceleration. Braking has no effect on it. Removed the tire, caliper, and rotor and found in and out play of the axle assemble. The backing plate doesn’t move at all. Just the full assembly going into the axle. Is this the cause of the sound?

ronjenx

There is normally some "in-out" play in the rear axle shafts. Mine has approximately 1/8".

Regarding the sound, have you checked for up and down play at the outer ends of the shafts?
How's the fluid level in the differential? Is it up to the fill hole when sitting on a level surface?