"Acceptable" backlash is what you're willing to live with. As you probably know, every regular screw has some amount of backlash. Since you always have to allow for it anyway by taking up the play in the same direction, by itself it's probably not a reliable measure of accuracy. At some point though, backing up the screw past the backlash and then feeding forward to where you want to be gets annoying.
Personally, I think I'd find that anything over about 30 thou would get annoying, but that's just me. Machines with a lot more backlash than that get used every day with great success. 10-15 thou would probably be reckoned pretty good.
Is the nut adjustable to take up the backlash? Trouble is, because of uneven wear that can go only so far. Adjust for minimum backlash in the center of travel, and it will probably bind at the ends.
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