Typically yes.
Some brands have varying degrees of primer hardness. I think general consensus is that Federal ammo has some of the softest, and Norinco surplus has some of the hardest primers.
However, in most cases the problems I have heard of result in light strikes, which can sometimes be solved with new springs for your gun.
It also depends on the specific firearm. Some firearms have free-floating firing pins, so that when the bolt slams shut, the pin continues forward and bounces off the primer. With soft primers and/or repeated chamberings of the same cartridge, you can get a slam fire. That usually happens with milsurp guns using commercial ammo, but can also happen with multiple chamberings of the same cartridge. The firing pin just keeps lightly hitting the primer until eventually it might discharge.
That is part of why milsurp ammo has harder primers, or you might have a lot more NDs especially with the guys who go out on patrol, chamber a round, then put that round back in the mag at the end of patrol.
If you have an old commercial gun, that's when I might be suspicious of using newer milsurp ammo, that might be made for guns with stronger alloys. But that goes for almost all old guns and new ammo, whether milsurp or not.