Well the nickel anti seize is what is recommended for Savage

I build a lot of AR's too and those hard core AR guys are ready to fight about mil spec. this and mil spec that. Only thing you can use on that barrel nut is this special moly grease.

I am a why not guy and use anti seize on the Savage and moly grease on the AR. Oil or grease or anti seize or nothing would probably work in either case.

But really why not. It sure can't hurt to follow the instructions