This is probably an easy one to answer...
Just docked at a new Campground and when I run the AC on a 30amp hookup the voltage meter in the rig goes down to 100 Volts and the polarity green light turns off. When I turn off the AC it EVENTUALLY goes up to 110 and the green light comes back on.
Is this an issue in my rig or with the power source?
Probably the campground's problem. Low voltage can damage things, so you may want to keep an eye on it. If you can, check the voltage at the pedestal. That will be a no-load check, but if it is low then it will be even lower when running the a/c.
100 volts kills things under load. I installed a Hughes Autoformer in the cord reel area for this reason. An progressive industries power watch would have shut off the power below 104.
Measure pedestal under load with roof air running. Don't push shore cable all the way into pedestal, so you have access to some of the copper prongs on the shore cable. Use a meter on those prongs.
Camp grounds are notorious for poorly wired pedestals. I worked one in California that had 120 vac at one end of a line of 8 site but it dropped to 104 at the 8th site. Nothing plugged in just leaks. Cleaned and tightened all the fittings but didn't help. Maintenance guy before me got credit for expanding one area into 50 amp sites. All he did was change out the power posts from 30 amp to 50. That worked well!
Another park in Texas had 12 50 amp sites but when all the big rigs came in on a Friday they turned on their ACs and everything blew at the posts. I had everyone unplug and checked the 200 amp breakers. one leg was 196 amp and the other was 20. Switched the A and B legs on every other post and got it better balanced to 110 and 90 but the real problem was the way multi-aired RVs are wired inside. Always check the post and ask others there is they are having any issues.
Both of these camp grounds were "name brand" and over 250 sites. Mostly poor maintenance.