how many thousands on bullet run out is acceptable.

I`ve been taught you want 0.005" max for hunting and for target or varmite 0.003" or less.
I`m not sure I can tell the difference at normal ranges between the two and don`t worry much about it. I simply try for the least I can get as I don`t turn necks, ect in search of the perfectly straigh round. This usually runs ~ 0.003-0.005 max with "most" at 0.003 or under.

This subject gets beat to death...and I'm unfortunately one of the beaters. Anyhow I'm with Ole Joe 100%. AND I can tell you that I know a very well known rifle builder in Texas that has the exact same goals for his reloading.
98% of your accuracy will come from how much your gun likes a bullet, powder, seating depth combo. You may get a slight "tweak" with keeping runnout under .002" for long range stuff.

I will beat it to death too. Big waste of time unless you have a match chambered custom rifle.
Spend your time where it counts most.

Less than .002 for paper punchers and less than .003 for hunting rigs works for me. Low run out will group better than high run-out in my rifles every time.....

Good Luck

Reloader