I don't think a change in barometric pressure changes a bullet's BC, but it does have a slight effect on trajectory which is the same result.
Well put. I agree and this can be a confusing point. Some shooters believe that the bullets' BC changes when atmospherics change, and that's one reason why you can never 'count on' a published BC (because it was established in different conditions and doesn't apply for your
conditions). The fact is that published BC's are corrected to standard
atmospheric conditions, and the ballistic programs count on this. When you use that BC in a ballistics program with non-standard atmospheric inputs, the program applies the effects of those atmospherics and the computed trajectory reflects the non-standard atmosphere.
do a lot of fancy math to figure out what the effective BC of the bullet is in your conditions, but that's just the long way around to get to the same thing.
You could do the math to figure out what your 'effective' BC is for a particular set of conditions, then leave the atmospheric inputs of the ballistic program at their default, standard values, but that would be self-defeating. Let the program do the math, that's what it's for.
Barometric pressure's not a significant influnce on a bullet's trajectory. Never has been, never will be.
On this point, I agree IF you stick to the same altitude above sea level. If you venture much to different altitudes, you will find the pressure has a drastic effect on trajectory. When I leave home (Michigan, near sea level) and travel to Raton, New Mexico (elevation 6000 ft+) for a long range rifle match, I use over 4 MOA (~45") less elevation at 1000 yards than I need back home. The difference in pressure is ~29.90 compared to ~24.00". If you stick to the same altitude, you'll never see changes in pressure this large but if you travel, don't underestimate the effects of pressure changes.