Could voters vote in either party's primary before? (I'm assuming they could, since otherwise those figures of yours are only explainable through heavy turnout swings - jsut askign to be sure)
Washington does not have party registration of voters. In a "blanket primary" voters can vote for any candidate regardless of party for
each office. Nonetheless, the votes were tallied as if they were for separate primaries to determine who went forward to the general election.
There was an additional little twist. Minor parties could only nominate one candidate. If they received enough votes (1%?) they would advance to the general election ballot.
This system was put in place around 1920, and had been used for 70+ years when the US Supreme Court ruled it unconstitutional in a California case that was later applied to Washington.
California Democratic Party v JonesCalifornia had recently switched to a blanket primary. California was somewhat different in that it had party registration, and also that voters could vote in the primary of any party. The decision noted a case where two Libertarians were contesting a race for a local office, and the combined total of votes was many times grater than the number of registered Libertarians. They argued that minor parties did not necessarily seek to elect their nominee, but rather use his candidacy to put forward certain issues, and that allowing non-members to participate, could dilute or corrupt the party's message.
For the 2004 election, Washington used a so-called Montana primary, where candidates from all parties appear on each ballot, but the voter indicates (in secret) which party's primary he wishes to vote in. This avoids party registration. Voters, of course might choose their party based on which party has the more interesting races, especially if it was for a top of the ticket office such as Senator or Governor.
Washington approved the new Louisiana-style primary in November. California voters defeated a similar measure. In both cases, opponents use the spectre of an Edwin Edwards-David Duke gubernatorial contest to encourage No votes. The difference in result may be that Washington was going back to something they were familiar with, it had the support of the Grange who had promoted the original system, and had never had party registration.