"...Can the M14/M305 fire normal .308 rounds..." Yep. I'd stay away from the Hornady Light Magnums though. Otherwise, any ammo that gives about 2800fps at 50,000psi will be fine.
Soft primers don't cause 'slam fires'. Poor loading techniques that leave high primers might. Mind you, in 30 some years, I've never seen nor heard of a slam fire.