Minnesota has four ballot-qualified parties. The two minor parties are the Legal Marijuana Now Party and the Grassroots-Legalize Marijuana Party. In Minnesota, all ballot-qualified parties nominate by primary.

Minnesota generally has secret open primaries. That means primary voters choose which party’s primary to vote in, in the privacy of the voting booth. However, Minnesota’s new presidential primary has different rules. Both the national Democratic and national Republican Parties don’t allow secret open presidential primaries, so the Minnesota 2020 presidential primary provides that voters must ask for a particular presidential primary ballot, and the qualified parties receive a list of the voters and which ballot they chose.

Presumably the two minor parties won’t ask for their own presidential primaries. However, even if they don’t, the Secretary of State has ruled that all four parties will receive the voter lists. The Democratic Party of Minnesota feels that parties that don’t actually hold a presidential primary should not get the lists. See this article. Thanks to David Sturrock for the link.