Rear wheel sideways "play"

Cheap wheels ill always have a little bit of play. But we are talking 2-3mm at the tyre. More is going to damage the bearings and risk braking the axle.

If its 2 months since you bought it it is warranty, so take it back to where you bought it and get them to sort it out.

But the stock Fuji Track wheels are very poor quality.

i think you have something against "cheap " parts. Nothing wrong with cheap parts, if you look after them and set them up properly.

As for "cheap wheels will always have a little play" is complete bollocks.
Sry to say it but i hate it when people say things which are untrue.