I shoot 7.62X51 (NOT necessarily 'NATO') in my FR8, and have shot some .308Win in it. No signs of lug setback. Gotta love the Kar98-based action.
My M1916 is a different matter - being nearly a century old, I handload lighter for it, using 7.62X51 brass - to about the same level as .30-40 Krag. No sense stressing the old action.
I once tried chambering handloaded 7.62X51 in my new-to-me Remington Model Seven (.308Win ) - it woun't chamber. Could be the 'once-fired' surplus brass was a tad long. I had not trimmed them, as they fit fine in my Mausers and CETME. Some commercial rifles have significantly tighter chambers. My .308Win handloads using the exact same dies (no change in adjustment) chamber well and are scary accurate in that rifle.
My old Spanish M43 Airforce Model is dated 1956, and was bought by me in 1976 - it's had thousands of rounds of 8mm Mauser through it - never a sign of lug setback. Reading the forums and other sources, I can find NO confirmed cases of the M1916 blowing up due to commercial .308Win loads. Handloads are a different matter - some will exceed SAAMI specs! I feel the old rumours of "soft Spanish steel" slander these fine rifles. The little 'cottage industry' cheap Spanish pistols are a different matter!