They are safe---they were originally 7.92x57 Mauser and this is not a wimpy cartridge!
However you do have to be careful about what they were re-barreled for. Mine is marked (stamped) 30-06. They were also changed to '7.62 Nato' when that became standard and are so stamped. The marking on gimp's was also used. Of course a 30-06 will not chamber in a 7.62N but the opposite is not so. I have been told that 30-06 stamped ones do not exsist but I have one, have seen others over the years.