Not sure how large your gen set is or which washer/dryer you have so it is hard to be definitive without additional information. My Newell has a 12.5KW generator so it can provide the same power as a 50 amp 240 volt service (ie 50 amps to each of the 120 volt legs of the service).
Assuming that your generator is properly adjusted and turning out a stable 60 Hertz, I can't see any reason you should not be able to run your washer/dryer on the generator. Most washer/dryer manufacturers recommend against running the machines while your coach is moving due to the additional strain on the bearings and spring balancing mechanisms although I have talked to RVers that do use their washer/dryers while they are driving down the road.
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Michael and Georgia Day
1992 Newell 43.5' #281
8V92 DDEC-2, HT740
PT Cruiser GT with Remco Transmission Pump https://newellowner.com/newell-photos/