We borrowed a friends Honda 2000EU generator last year. First time ever using a gen.
It was hot and muggy during the day, but not bad at night, so we didn't "need" A/C at night.
Since we had the gen to use the A/C, it was running at full throttle. Found out that the vaunted "quiet" running of the Hondas is when they are on "eco" mode and basically only idling (charging camper battery and using fans, other light electrical loads). To run the A/C they have to be at full throttle. When running at full throttle, the Hondas are not as loud as an open "contractor" generator, but they are not quiet.
We didn't start up the gen until 8am, and shut it off by dark - around 8pm.
I did talk to a neighboring camper who was using a tent. Fortunately the sites were large and had good separation. I told him when I would be running the gen, and if he had any issues to please let me know. He seemed to appreciate the talk, and we had no problems.
Besides following campground rules, running generators I think is very dependent on the situation. If it is a quiet, cool afternoon - do you really have to run the gen? Even if it is within the proper time, it is just not needed.
If you were "first" to a camping area with limited rules, and basically was able to run your gen whenever, when someone else sets up after you please don't claim "first dibs" and run your gen all night. I would use discretion and shut down the gen at a reasonable hour, and start it up late in the morning - or even wait until afternoon. This is all situational. If the neighboring camper walks over and asks if it is okay to run his gen at night, then go for it! You both run your gens over night and bask in air conditioning.
Pretty much everything regarding camping and noise is common sense and being aware of your surroundings - especially neighbors.