Effort in South Dakota Aims to Drop Parties

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3. California has a modified open primary to avoid Constitutional issues

California has adopted a new modified open primary that only applies to office holders rather than Presidential delegate selections.

A third alternative is the "modified closed primary", as has been in effect in California since 2001. In California's primary since 2011 the voters are allowed as individual citizens to vote for any candidate, and the top two candidates regardless of party will advance to the general election. The Presidential election is exempt as it is a contest for delegates rather than a direct election for an office.

Prior to the California election reform of 2011, each political party could decide whether or not they wish to allow unaffiliated voters to vote in their party's primary. This appears to avoid the constitutional concerns of both the open and the closed primary. In the 2004 and 2006 primary elections, the Republican, Democratic, and American Independent parties all opted to allow unaffiliated voters to request their party's ballot. However, since the 2008 presidential primary election, only the Democratic and American Independent parties took this option, while the Republican party did not.[10]

https://en.wikipedia.org/wiki/Open_primaries_in_the_United_States

For Presidential elections if you are registered with NPP(no party preference), before the primary, they will send you a card to select which ballot you want, a republican, Democratic, or independent ballot, etc. There is no mixing parties within a ballot for Presidential election primaries