I am currently living in Washington State but maintained residency in California as my real estate license is there and I want to be able to collect referral fees from California real estate sales. I am living with my daughter and own no property in Wash and am retired. Is this legal?

Sure, I see nothing wrong with this. You continue to be a California resident, although you are physically in Washington.

But, contrary to what the title of this thread says, you do not want to establish Washington residence. In other words, don't get a Washington driver's license, resident hunting or fishing license, register to vote there, etc.