Assuming CM steel that was recently threaded at the muzzle and left in the white, how do you normally address fending off corrosion under your suppressor or brake? Cold bluing? Some other route?

Grease.

I use the stuff that I also use on my shotgun choke tubes.

Anti-seize

I wouldnt worry about it

+1

Marine grease.

Oil

I use oil

anti-seize. You are going to get carbon buildup on the treads that can make the can hard to remove.

I've been using a dab of Shooters Choice grease on my other threads when the cans are on the direct thread mounts, but they're all SS or nitrided barrels, so I was not concerned about corrosion, just keeping things from freezing up. None of these are high-volume semi-auto applications, and the cans get moved around a bit.

i'd prolly cold blue the threaded portion then use a dab o grease on em.
Big Ed

Copper based anti-seize, the gray will dry up and blow away over a period of time

Remember, if you use anti-seize, no matter how careful you are, it’ll end up everywhere..😁