"The general doctrine that a marriage valid where contracted is valid everywhere, has so often been declared by the courts and reiterated by text writers that it has become a maxim of the law.
But there are exceptions to the rule as well established as the rule itself, viz: (1) incestuous and polygamous marriages prohibited by natural law; and (2) marriages prohibited by positive law." State v. Nakashima, 62 Wash. 686 (1911).
"Marriages in Washington are prohibited between parties nearer of kin to each other than second cousins, either of the whole or half blood, computing by the rules of the civil law. Wash. Code § 7151" [renumbered: RCW 26.04.020(1)(b)]. Nakashima, at 687.
The existence of positive law prohibiting a 1st cousin marriage in Washington State, under Washington law, would render a valid California marriage void. However, it is worth noting that ehe applicable case law I have provided is exactly 100 years old. The point being that the issue rarely arises -- and, since a marriage annulment requires a court order, unless and until you or your spouse were to challenge the marriage, it is unlikely to ever arise as an issue.
http://www.justanswer.com/family-law/5n8yz-married-1st-cousin-calif-legal-state-moved.html