FWIW:
Back in 1973, my brother and I were in a gun club and an elder gent had an honest to goodness National Match M-1, in as issued condition. He let us shoot it with the only '06 ammo we had, some Rem 180gr Cor-lok "round-nose" soft points.
After seeing both my brother and I put 5rds each, into a 6" bull "off-hand" at 100yds with it, he said, let me see that thing, and proceeded to shoot the other 10rds from the box. (He later gave us both a box of "vintage" National Match 173gr ammo- I still have it !!!). He got a 2" group shooting from a "rested" position, but not benched or bagged. He stated he'd shot the gun in competition in the late '40's including the Camp Perry nationals and never seen anything shoot as well through that rifle.
The 180gr RN C-L's are Remingtons "Not so Well-Kept Secret" amoung those who have shot/tried them.
They are loaded the same way they've been loaded for many years, and shouldn't hurt your M-1.
The only commercial ammo I would avoid is the Hornady Lite-Magnum as it possibly could damage the action rod.
All other is SAAMI spec. so shouldn't hurt the M-1.
I would be more concerned about a lot of the old "mil-spec" ammo that is being imported and sold that is not loaded to any known "standards".
My brother now has an M-1 that he's owned since the mid '80's and has shot service rifle with it, and it too shoots the Rem C-L very well. He wouldn't shoot anything in it that he thought that would possibly damage the op-rod. He's convinced that the Remington won't.
But if still in doubt, contact Remington and see what they say and let us know what they said........