For readers interested in the genesis of the Democratic Party of Hawaii's potential legal challenge to the state's open primary system, a good place to start would be the party's constitution, its governing document.
From Article I, Section 1. General:
The Democratic Party of Hawai‘i shall be open to all persons who desire to support the Party, who wish to be known as Democrats, and who live in Hawai‘i.
The Democratic Party of Hawai‘i believes that its primary election, a state-imposed mandatory nomination procedure, ought to be open to participation of only such persons as are willing to
declare their affiliation with and support for the Party, either through public registration to vote, or through maintenance of membership in the Party. The Party further believes that the current
Constitution and laws of the State of Hawai‘i, by maintaining secrecy of affiliation, and by compelling the Party to admit to its nomination procedures those who may have no interest in, or
actually oppose the interests, values, and platform of the Party, do violence to the Party’s associational freedoms and the individual freedoms of its membership to define their own
political views, guaranteed under the Constitution of the United States. The State Central Committee and Party Chairperson shall take appropriate action to correct this injustice.
Hawaii is among the minority of states with open primary systems.
While voters in the islands may describe themselves as Democrats and Republicans, most do not officially belong to either political party. Voters are also not required to declare their party affiliation when they register to vote with the state, and are free to choose between the parties during primary elections.
The Democrats' lawsuit, if successful, would require voters to declare their affiliation before voting in primary elections.