Technically, it's not great for them but really it's a minor enough issue. I wouldn't worry about it. Honestly as many times as the campground power fails or runs low voltage, you are probably less likely to do damage letting the generator run out of fuel.
I might differentiate between the newer inverter generators vs older analog generators.
- The inverter generators will usually force it to hold voltage until it can't and then cut out (ie: the cut out is abrupt more like flipping a switch to cut power).
- Analog may surge as the engine is dying with both voltage and hertz varying for 10-30 seconds as the engine is running out of fuel. The result is the electrical devices must adapt (or be damaged) during this time...some devices won't care other will.