What is acceptable for one person may prove to be categorically unacceptable to another.
If you plan to use the machine as a drill press, it is probably fine. For simple milling and facing, you could probably live with it. If you will do precise hole location drilling, groving, slotting or other work needing precise table positioning for size control, it is unacceptable.
For example, we had 0.001 backlash on our ball screw equipped machine. It was ok for general machine work. We then tried to precise form milling (putter heads) and the B/L left "flats" at direction change points which ruined appearance.
With gib adjustments and ball screw bearing shimming, we got B/L accelptable for putter milling but it was still too much at 0.0003" for master form shape milling.
We then had the ball screws reworked and replaced ball screw bearings with special ABEC 7's with high preload ones. Now we have B/L comp'd out to near zero.
We still see a 0.0001 error at direction changes while profile milling but it is "acceptable" but not what we ultimately hoped for.
At this point, however, we'll need to change software, servo encoders, ball screws (from rolled thread to precision ground) and PC and controller card to noticeably improve performance. Since this will involve close to a $10k investment (to eliminate a 0.0001 error that we can live with), we've stopped making improvements for the time being.
Ultimately, YOU will have to decide if the backlash you're seeing is "acceptable". For our use, however, it would be about 100 times too much.
Drill press or precision mill - the choice is yours and the ca$h therapy applied to turn one into the other is the controlling differential between the two.....