The primer in your example picture is what is called a "cratered primer".
This is quite different from an unfired primer not seated fully.
Are they safe to shoot?? well, you did, and the world didn't end, did it?
(sarcasm intentional)
What the cratered primer usually is, is a sign of high pressure, however, it can also be caused by an overlarge firing pin hole.
What I mean by high pressure is essentially this..
a degree excessive pressure for that primer/that firing pin channel
this is usually, but not automatically overpressure compared to the standards. It is, however, overpressure for that particular load components. Primers vary, and a load that is normal looking with primer A COULD show pressure signs with primber B if B is made of a softer/thinner cup metal.
Back off the load (10%) and try again.
If you are shooting a load that didn't do this with a different primer brand, and only have 20rnds or so left, its unlikely the pressure is high enough to damage your gun, but DO check your already fired brass for case head expansion. Safest thing to do would be pull the bullets and reduce the powder charge.
I have shot rounds that did that, but I won't recommend it to anyone as being completely safe. I think it is, but I don't have your gun or your loads, so if you do shoot them, its all on you.