Paul,
300 norma Magnum is fine on a Remington action. The Remington lawyers let them build and sell 338 Lapua Magnum on a stock Remington action. 300 NM has quite a bit less thrust. If lawyers are anything, they are risk averse. I'm getting ready to build a 300 NM Improved for myself on a Remington Short Action single shot action. I had a long action prepared for it but decided i want it single shot.
I know lots of people say lots of things and much of it is from "I read it on the internet", but there is no way a Remington action threads, or any other heavy action threads, will fail from 100,000 normal rounds of 338LM. The lower action lug would be the first to go because it has very little backup material, but this would not be catastrophic. Anyone who has had an action fail had a squib or a reloading error (or a cleaning rod. I don't bring cleaning rods to the range). There was recently a 375 cheytac fail and blow apart. After they picked up the pieces and the threads were mangled, there was speculation that the gunsmith did a poor threading job. I guarantee it was a squib or similar. Threads will of course look horrible after failure.
Because I can, and because many recommend it, I am going to recut the threads on the Remington action to 1.125 x 16 (from 1.062 x 16). Hey, machining is fun and if I ever sell it this will be a selling point. It gives you more thickness in the tenon.
I'm building a 33XC on a bat action, again with 1.125 x 16 threads. It is long action single shot. I would have built it on a Remington action but they don't make long action single shot.
--Jerry