The "official" grease for the M14 was Plasti-Lube which is a brown grease that was packed in M14 cleaning kits.
grease was GAA (Grease, Automotive & Artillery) available in every GI motorpool and maint unit. Not quite as long lasting, but just as good while it lasted.
Issue "rack grade" guns do not suffer from full disassembly. Tuned "Match" guns, glass bedded, should not be taken down unless necessary(spring replacement, etc), as damage to the bedding can happen unless you are very careful. And the more often done, the "looser" the fit becomes, even if you are very careful.
Not important for combat accuracy, but for winning a match, every little bit counts.