Yes -- You can even buy homes in foreign countries if you wanted too. Are you going to live in the home as a primary residence, is it going to be an investment (rental) or second home -- and are you active duty military? If it is a second home and you spend the majority of the year in Washington and claim that to be "home" -- it should not change your current state residency. Contact your local government and ask the questions. It is best to be informed by the people to enforce the laws in your State!
Yes, you can buy a house in California even if you are not a resident. Many people purchase second homes or investment properties in other states. Buying a home does not automatically change your residency, but how much time you spend there could affect things like taxes, driver’s license, and voter registration. Because residency rules vary, it is always best to confirm the details with a tax professional or attorney before you make a move.