There are several comments here about problems between the charger and an Onan generator. Those problems often disappear when the gen is loaded. Similar problems are often found when the gen is an inverter gen. The oldest Onans used no voltage regulation at all. The faster they spun, the more the output voltage. They were set at 60 Hz to produce the desired output voltage. The CCK model comes to mind.
Newer gens, including the Onan Marquis series, many Generacs and most other high end gens use a chopping type voltage regulation to control the current through the excitation windings. At low voltage, this seems to make some charger circuits unhappy. Many chargers need the top end of the sine wave voltage to work well. At low loads, some generators don't meet the needs of these chargers.
The most expensive generators (Onans Quiet Diesel series and fancy portable gens) use an inverter to produce the output AC waveform. Again, some chargers just aren't happy with the output from these generators, particularly at low load. it depends quite a bit on the design of the charger's input circuit as to whether there is any problem.
I happen to love my 40 year old Onan CCK. It has no fancy electronics that interferes or interacts with the electronics in chargers and microwaves.
