Define better "side to side play." If it's movement of the shaft in the hole, then you're probably fine. If it's "in and out" - maybe not so fine.
Um. Look over Tom Endy's instructions for rebuilding the Model A rear axle.
If "in and out" it's sounding like you have "extra space" somewhere between the axle shafts. Possibly in the housing bearings, possibly in the differential carrier (which "pins" the two axles together and causes them to face the differential spider gears.)
In and out not sounding that good - how does the rear axle sound otherwise? Noise would probably be between the pinion and ring gear. But there could be a lot of free play in the differential carrier part which you never hear - except when you turn a corner.
https://www.santaanitaas.org/wp-cont...vised-2014.pdf
Joe K