Meh, grease is too cheap and plentiful not to use the right stuff imho.

Much like what lube to use on the rest of the gun, lots of people get off in the weeds about "I only use the proper mil spec grease on mine" bravado.

It's a fastener. Torque spec is a wet spec with their grease. Find something remotely  close, smear it on, torque and loosen twice before applying your final torque. Done. No need to overthink it.

Aeroshell 33MS on all my barrel nuts. Always.

Not disagreeing with you there. Just trying to clear up some age old misconceptions regarding why to lubricate threads and what actually leads to galvanic corrosion.

In regards to "anti-seize", the two primary contributors to seizing are galling and/or FOD. In this context, the Type 3 anodization does a nice job of preventing galling between steel and aluminum; the greatest contributor in AR builds is FOD on the threads. Clean threads + any lubricant should prevent seizing.

Regarding why to use MoS2 based grease, have to go back to preload uncertainty. Dry threads, in practice, generally carry a +/-30% bolt tension force range when torqued down (can depend on who you ask, folks will carry anywhere from +/-20% up to +/-35%). The use of any grease type lubricant can drop that uncertainty down to +/-10%, if not closer to +/-5%. MoS2 based greases then also minimizes friction better than most regularly available and easily applied lubricants. In short, it allows you to achieve a higher bolt tension force for a given torque with a tighter uncertainty range.

I'm not sure about the numbers but the concept makes a lot of sense to me.

There are several factors that come into determining what uncertainty range to use. In the case of bolted joint analysis, if the application can afford it, using a wide uncertainty range for calculating margins is decent CYA method.

Generally speaking, the larger the thread size the less uncertainty, so given the AR barrel but thread size, it's probably safe to say the dry uncertainty is closer to +/-20%. But the use of lubricant will drive that down.

It's also worth mentioning that with the spec torque values, even assuming worst case preload with dry threads, it's nowhere close to yielding the 7075 threads on the receiver.

Amsoil NLGI #2 Multi-Purpose because it's what I use when packing wheel bearings and lubing U joints. No special grease required.

Again, makes sense.  As long as the actual achieved torque is well below the design strength of the threads on the receiver and nut, I can't see how lube could possibly hurt.  It seems that lube might only be a problem when dealing with the upper end of the yield curve which, as you say, isn't an issue.

I built two uppers today and I assure you my nuts will not seize.

Wheel bearin grease  

My thoughts as well.

Most likely it is fine.

The original grease has changed a couple of times, from non-synthetic EP, extreme pressure moly grease to synthetic extreme pressure EP moly grease.

There is an automotive synthetic EP extreme pressure moly grease that is, "gray" in color, with moly, just not quite as much grease as aircraft landing gear grease.

https://shop.advanceautoparts.com/p/valvoline-moly-fortified-gray-full-synthetic-grease-1-pound-vv986/7070009-p?product_channel=local&store=9029&adtype=pla&product_channel=local&store_code=9029&gclid=CjwKCAiAsYyRBhACEiwAkJFKosDx6dp4JWhpY8qgCvLrcqEhMK6w76YqICglXSoFcgsM4kJX0EwTzhoCGmAQAvD_BwE&gclsrc=aw.ds

The specs should be close enough for torquing a barrel nut to an aluminum receiver.

I use a brush or a swab and grease the threads and the barrel extension out and / or receiver inside, where the steel barrel extension contacts the inside of the receiver, long with the outside threads.

Note some hand guard rails have aluminum barrel nuts, instead of standard steel barrel nuts and may have very different specs.

I use a dab of grease on the flash hider threads, if I'm not attaching a suppressor mounting flash hider, but light gun oil would work for the flash hider threads too though.

Just a tiny amount of barrel nut grease on the back of a flash suppressor makes tightening up a crush washer a lot easier.