Most any heat and water resistant grease will work just fine.
Many shooters just buy tube of Lithium grease at a hardware or farm supply store or Walmart.
The "official" grease for the M14 was Plasti-Lube which is a brown grease that was packed in M14 cleaning kits.
Disassembling your Service grade M1A won't harm it, but better to not do it too much.
Match grade M1A and M14 rifles are often literally glued into the stock and are never disassembled except for re-barrel and rebuilding.
These have all maintenance done with the rifle assembled, including greasing.
One pointer in case you aren't aware of it. You can buy or make a bolt roller grease tool to inject grease into the bolt roller.
You can buy the tool from Brownell's or you can make one from a 40 caliber pistol case.
Just thoroughly clean the case out to get any dirt out of the case AND the primer.
Pack the case with grease and force it over the bolt roller. The pressure will force grease into the roller and prevent wear or breakage.