Washed coyote pelts look 100% better IMO. The white looks white instead of beige and the fur gets all thick and fluffy as opposed to flat looking. For me it's an important step in the process but to each their own.
NAFA doesn't say that it has to be done but to me it sounds like they think that it might be a good idea to do. From the NAFA pelt handling manual:
"While washing is not needed for all pelts, it does improve their appearance. Removing mud, dirt, or blood will give the fur grader and buyer an accurate assessment of the pelt’s true value. Washing also loosens matted fur that has been crushed by Conibears and snares that would have left obvious breaks in the fur and a lower pelt value. Washing in cool water with a little soap will not remove the pelt’s natural oils. Too much soap will leave a dull, “dead” appearance to the fur by removing the pelt’s natural oils."