The Durango Herald has this explanation of Colorado’s proposition 108, which would require parties that polled 10% in the last gubernatorial election, and which therefore have primaries, to let independents vote in their primaries. However, the parties would have the option of giving up their primaries in any particular year and nominating by convention, but only if 3/4ths of their state central committees agree to do that.
Under current Colorado law, independents can decide on primary election day that they want to vote in a major party primary, but to do that they are technically joining the major party whose primary ballot they choose. Proponents of the initiative say some voters are conscientiously opposed to taking that step.
Also under current law, in rare cases, the ballot-qualified minor parties (Libertarian, Green, Constitution) have primaries for a few offices. This only happens when those parties hold a nominating convention and two candidates for a particular office both make a strong showing at the convention. It has never happened for a statewide office. Proposition 108 would not change that, and qualified minor parties could still choose not to allow independents in these occasional primaries.