On April 17, the Wisconsin State Board of Elections (which is formally named the Government Accountability Board) ruled unanimously that it has no authority to remove candidates from the upcoming Democratic primaries, in the special gubernatorial and legislative recall elections, just because those candidates aren’t loyal to the Democratic Party.
Some individuals are running in the Democratic legislative recall primaries because, by guaranteeing that there are at least two Democrats running, the state must hold a Democratic primary, and that has the indirect effect of postponing the election itself from May to June. These individuals, from all the evidence, are partisan Republicans, and the Republican Party doesn’t want the special legislative elections to be in May; instead they want them in June, at the same time as the gubernatorial recall special election.
But, Wisconsin has had an open primary since 1907, and has never had voter registration by party. See this story.