The term “open primary” in California’s Constitution, relating to the presidential primary, was passed in June 1972 as Proposition 4.
The Legislature wrote it and put it on the ballot. It plainly relates to which candidates should be on the ballot, not which voters could vote in any particular primary.
This is obvious from how it was presented on the ballot: “Proposition 4. PRESIDENTIAL PRIMARY. Requires primary election wherein all recognized candidates for President are on ballot unless affidavit declaring non-candidacy is filed.”
The arguments in the June 1972 Voters Pamphlet talked about which candidates should be on the ballot. It is just a linguistic accident that the drafters thought a good term for forcing all presidential candidates to appear on the ballot, unless they swore they weren’t running, was “open primary.”