After inquiring the Washington Department of Fish and Wildlife, I was provided these links regarding the lists of illegal and banned animals in Washington.

Most of them are bans on aquatics, like nuisance fish, frogs, salamanders, mudpuppies, mussels, turtles, etc. Nothing about venomous snakes, etc that I could see, and nothing about other reptiles. The exception being anything native; you cannot capture wildlife and keep as a pet from Washington, they must come from out of state and be documented as such.