The Maine Green Party (whose name is the Green Independent Party) has voted to allow independent voters to vote in its primaries, and they need not join the Green Party. See this story. The two major parties in Maine also let independent voters vote in their primaries, but only if they join those parties at the polls on primary election day.
Now that the party has taken this step, it will be in a strong position to argue that independent voters should also be able to sign petitions to get members of the Green Party on the party’s primary ballot. Maine and Massachusetts have the most draconian requirements for members of small qualified parties to get on their own party’s primary ballot. At least Massachusetts lets independents sign such petitions; Maine does not. The Maine Green Party has never been able to nominate any candidates for either house of Congress since it has been a ballot-qualified party, nor has it been able to nominate anyone for Governor in the last two gubernatorial election years.