Hi, Welcome! You are sure to get many replies. This topic pops up frequently. I'll tell you that I just got back from a 14 day 2008 mile extravaganza from Ohio, to FL to visit the land of the Mouse and Fort Wilderness, and back via Gatlinburg and the Smoky Mountains. The fridge stayed on auto the whole time. Saved us one evening when we tripped the breaker on the post at a campground while we were away. Fridge switched to the battery and LP. No issues.
The units are designed to run on gas while underway. I don't think I could have kept every thing cold during the heat of the day on several legs of our travels, especially the last day, which was an 11 hour dash for home, any other way.
So. I use it as it's designed to run.
You may run into places that require it to be off. I have not yet encountered one of these places. I know they are out there though.
(No, I didn't turn it off at gas stations either. Sorry! I did use outside pumps or RV lanes pretty much the whole trip.)
Welcome again! Happy camping.