I was able to find SAAMI's specifications for ammunition but I looked all over NATO's website and couldn't find what military specifications are for ammunition or anything else is. It is probably there somewhere but I didn't find it. Is there another place to find it?
While I can't really believe anyone loads ammunitions at much less than commercial specification, except when someone says it is, just because they don't know what it might be fired in, there are some things that are reasons for caution. Not so much for loading the ammuntion lighter, at least for that reason, but for other reasons. I'm thinking here of rifles that have been rechambered. I thinking here of some Spanish rifles that were Model 92 and 93 Mausers, not the Model 98. But some of these rechambering were made over 50 years ago, so if there were serious issues from a safety standpoint, surely we would hear more about it and maybe not. The Spanish used a special, lighter loading of the 7.62 NATO and I think maybe the Japanese may, though I didn't run that down before making this post. Anyway, a lighter loading would presumably not create any safety issues with converted 7mm rifles.
There is commercial .308 ammunition that is loaded lighter and advertised as such, though I don't know the reason that sort of ammunition was produced.
There are, however, distinct military loads of 7.62 NATO but nowhere near the number of different commercial loads. Belted (meaning loaded in belts) ammunition is also not loaded the same in different countries. British ammunition has a high proportion of tracer rounds, for example, but it's entirely useable in American weapons, which is the whole point of standardization.