Slight axle end play is completely normal for axles retained by C-clips on the inner ends of the axles, which is the system used by almost all Chevy rear ends except a few heavy-duty 1/2 ton Dana/Spicer axles in GMC camper rigs.
Unless it's making really loud grinding noises, I'd suggest pulling the rear cover and doing a good flush with spray solvent, replace the cover with a new gasket, and refill it with fresh lube. It might cure the problem, and even if it doesn't, you're only out of pocket for a gasket, some solvent, and a couple of bottles of 90 weight.
Jerry
