How critical is the quality of the barrel nut?

[sharpshooter]

Thery are made on a bar fed cnc lathe. A bar feeder pushes stock through the headstock of the lathe. The tools do all of the work as it is held in a rotary collet, so all of the operations are done in one fixturing. There are bored, threaded, faced, contoured and milled before they are cut off. A secondary axis picks off the part and deburrs the tapered end.
So the business end is always square with the threads. You may notice on some that there are some minute burrs left from the slot milling operation on the face, but that can be remedied quick with a couple of swipes on a stone.

[Savage6x284]

Thery are made on a bar fed cnc lathe. A bar feeder pushes stock through the headstock of the lathe. The tools do all of the work as it is held in a rotary collet, so all of the operations are done in one fixturing. There are bored, threaded, faced, contoured and milled before they are cut off. A secondary axis picks off the part and deburrs the tapered end.
So the business end is always square with the threads. You may notice on some that there are some minute burrs left from the slot milling operation on the face, but that can be remedied quick with a couple of swipes on a stone.

As I expected they were.
I've rejected countless parts made precisely like this using some of the finest European and Japanese live tooling, bar fed CNC lathes.
They can, and do, make out of tolerance parts. With the modern CNC lathes an operator can make a BUNCH of out of tolerance parts very rapidly.