Clarification: 3/8" is the nominal size; actual major diameter is 0.662". 18 threads/inch.

"Everyone is entitled to their own opinions, but they are not entitled to their own facts."

Thinking about the media size that would be needed to get into the valleys.....no longer "shot", more like some form of abrasive.

NPSM can be rolled.

That's precisely my concern; these are very small threads.
There is a shoulder at one end of the part that precludes rolling. Which leaves only inferior cutting.

"Everyone is entitled to their own opinions, but they are not entitled to their own facts."

Looks like a 3/8" pipe thread.
What is the material, and what is the environment ?
Is it possible fatigue cracking is a concern? Perhaps because a heavy gauge is going to be mounted on a long pipe spud, inviting a nive low "reed" frequency ?

In some industries Shot peening threads has a good reputation for reducing galling tendencies.
"So, for oilfield tubular connections, both the cut and rolled threads require a final surface modification treatment of controlled shot peening."
http://www.mfn.li/article/?id=390

The materials are SS304 and Inconel 600.
Fatigue is not a concern.
The joint is expected to be connected once only during the lifetime, so is galling much of a concern?

"Everyone is entitled to their own opinions, but they are not entitled to their own facts."

Lubricants not permitted.

"Everyone is entitled to their own opinions, but they are not entitled to their own facts."

What are the shot peening specifications ?
Glass beads come in small sizes and can be used to peen threads, small features and delicate parts.

Is this a tapered pipe thread, or a straight pipe thread?
Either way, If truly unlubricated assembly, Galling at assembly can ruin your day.

If tapered, a liquid tight seal is expected, so teflon tape or pipe dope will be applied at assembly. Both have powerful lubricating effects.

Note the low galling resistance of unlubricated 304 against some materials in Table XI here -
https://www.nickelinstitute.org/~/Media/Files/Tech...

This 1979 report has some tests of 304 fasteners and "heat treated" Inconel.
http://www.iaea.org/inis/collection/NCLCollectionS...
The parts were pretty aggressively degreased.

In Table 1 it looks to me like 304 on Inconel either tightens unscathed ( Visual 1) or goes to hell ( visual 4 and 5 ) .

If truly assembled unlubricated, then the galling resistance of peening suggested by the previous link to oilfield practice makes sense to me.

Section 3-3 here -
https://www.shotpeener.com/library/pdf/2001012.pdf

There is no shot peening specification yet, just an idea.
Straight thread, NPSM per ASME B1.20.1. Actual thread height is only about 0.036".

"Everyone is entitled to their own opinions, but they are not entitled to their own facts."