If you literally move to Washington and make it your new main, permanent home (your domicile in tax terminology), then your W-2 income from remote work carried out in Washington is not taxable by California.
Once you become a non-resident of CA, CA can tax you only on CA-source income. Remote work carried out outside CA is not CA-source income. Work is sourced where the work is actually performed.
You can find CA's detailed rules for determining your residency status in this web reference:
https://www.ftb.ca.gov/forms/2019/2019-1031-publication.pdf
But if you work as an independent contractor (your income is reported on a 1099-MISC instead of a W-2), and you provide contract services to a business located in CA, that income would be considered taxable by CA.
**Answers are correct to the best of my ability but do not constitute tax or legal advice.
