The differences between 7.62x51 vs. .308 are not the same issue of 5.56x45 vs. 223.
7.62x51 really is less pressure than .308 - 50,000psi vs. 62,000psi. Using any kind of military rifle (including the M1A) its important to stay around 50,000psi, due to the fact (eg) the M1A/M14 uses a gas port in the barrel to draw off a certain PSI to cycle the action. Using the right powder (with the right pressure curve) is important for this reason. IMR4895, H4895, Varget, IMR4064, RL-15, all are close, and will safely make 7.62x51 loads.
Basically the 7.62x51 for your M1A akin to M2 Ball for your Garand. Commercial ammo won't blow it up, but it'll work the action a bit too hard.
The issue of 5.56x45 has to do with the long, heavy 62-grain bullets jamming against the rifling of .223 varmint guns (built with small amount of freebore) made to shoot < 50gr bullets leading to excessive ("higher") pressure.
Edit RE to "de Witt":
Tell that to the fine folks at Hornady which devote a section to ".308 Service Rifle" with loads not exceeding 50,000psi or so. That is according to SAAMI test standards. NATO's test practices, different units of measure, etc., doesn't apply here.
Like I said, 7.62x51 is to .308, what M2 Ball is to .30'06. The same, but different.