Hi, first time post here. This thread is old, but it is the first to pop up on a Google search. I too have a stainless steel barrel, receiver, and barrel nut and was looking for the right anti-seize to use. The Permatex website says their "Aluminum Anti-seize" contains aluminum, copper, and graphite. I agree that copper is a no-no, so I e-mailed the company to see if their description was a generic one for all their products or specifically to their aluminum anti-seize. The e-mail I got back said; "For stainless steel and other similar metals we generally recommend out [our] Nickel Anti-Seize. Our Aluminum Anti-Seize does contain aluminum, copper, and graphite so there is a small amount of copper in it. Generally copper only enters into the SS during times of high temperature or pressure. For most applications this will not be an issue but if you are at all concerned then we recommend our Nickel Anti-Seize. -Technical Services ITW-Permatex."
So, maybe not the best for SS. Not sure if the barrel nut torque or gas leaking through the treads is considered high pressure/temperature. I've compared most other posters' recommendations to their perspective MSDS forms to look at ingredients. If it is true, what other posters say, that teflon, lanolin, graphite, copper, and lithium are bad, moly-grease grows acid producing bacteria, and nickel is a carcinogen then there isn't much left that would be safe for stainless steel that isn't harmful (nickel being a carcinogen). For me, that leaves: generic greases, Loctite Heavy Duty or Food Grade, and Pro-Shot Pro-Gold grease lubricant.
Hope this clears up any confusion about Permatex Aluminum Anti-Seize.