Agree with Pdvdh.
Consider that many typical centerfire rifles run somewhere around 50,000 to 60,000 ksi.
Sea level atmospheric pressure is roughly 14.7 psi or less than 0.027% of that pressure.
So, if the total effect of atmospheric pressure is that small, consider how a change in that atmospheric pressure makes in the total pressure.
Typical ballistic piezo gages or strain gages would never detect the difference.
That is the internal ballistic pressure issue, that is not to say that ambient pressure isn't very important to external ballistics.
Ambient air density has very little effect on internal ballistic pressure, but ambient temperature does.
Temperature has an effect on the combustion pressure in two ways. The propellant initial temperature affects the combustion and peak pressure and the ambient temperature affects the speed of sound in the surroundings.
The typical temps, altitudes and pressures while hunting are one thing, the ones we designed for in modern military aircraft are another.