I have had the HF (Harbor Freight) 800/900 generator for about four years. I also have two Champion 2000 inverter generators and a built in Onan microquiet generator.
The HF unit will power a battery charger, no problem. It is louder than an inverter generator but not as bad as some claim. It is 2-stroke requiring oil and gas mixed but it is NOT as loud as a weedwacker or chain saw.
I use mine mostly around the yard to power an electric chain saw or an electric lawn edger.
If it will be used in a noisy environment around other people making noise there would be no issue using the HF unit. It may not be received well in a quiet campground.
I bought mine for $75 at a parking lot sale plus used a discount coupon. While HF will allow a discount coupon on sale items, I think generators are now excluded. To find the best deal currently, check on
https://slickdeals.net/f/1276399-harbor-freight-coupon-thread.