I have the same rifle but in 7.62x51. I use plastic training rounds through mine that provide respectable accuracy out to at least 25 yards (furthest I've tried so far) and they are quite "blasty" (10gr bullet at 4000 fps from what I've read) and inexpensive ($8/50).
However, if I were wanting to fire some 7.62x51 through it, I wouldn't be concerned and would do so. In fact, I probably will fire off some 7.62x51 DAG FMJ that I've stock up on.
It's the .308 Winchester that folks might want to reconsider firing through their 1916 Civil Guardia Spanish Mausers, especially the fodder advertised as being especially high velocity or "light magnum".
If my Spanish Mauser remained in the original 7x57 chambering, I wouldn't have the slightest concern firing that through it. It can be found, and though not cheaply (as in military surplus), it is in most cases affordable (as in commercial PPU).
It's a shame some treat the Spanish Mauser like a pariah from some leper colony simply due to the lack of the 3rd "safety" lug. Keep the rifle in good working order, inspect the rifle before every outing, keep the ammunition sensible and you're good to go. Keeping within these guidelines, the rifle will likely outlast you.