Are you measuring this with a tool ???

A TS-Aligner would be good for that.

A arbor is not supposed to move in any direction.

This "sounds" like the arbor bracket might be screwed, if
the bearing are good.

kansascats wrote:
The arbor on my Jet cabinet saw seems to have about 2-3 thousandths of
side to side play. I pulled off the belts and the arbor can be moved
side to side in the arbor bracket.