Can I use a small propane instant hot water heater for a clothes washer?
Modern washers have a timeout (in case the water-fill sensor fails) which is around 10 minutes, but you'll have to check the manufacturer to get the exact timeout for your washer as well as how much water it needs to fill at your preferred load settings.

If (DesiredCapacity / HeaterGPM) &lt; TimeoutInMinutes

...then you'll be ok (I wouldn't cut it very close though - it would be a bummer to see it time out one millimeter short of full) So if you had a 10min timeout and needed 10gal to do a tiny load with a 1.5GPM heater:

10gal / 1.5gpm &lt; 10min ? True.

... to be fair, a maximum load of a washer is typically 40gal so the concerns would be reasonable.

Because of all of these variables, those who make the washer would know best since they would know these variables.