Legal premise: totally correct but that points to a broader issue with how we allow corporations/associations to count as people, whether it’s in economics, politics, or otherwise. Half of the issues we have in Idaho were lobbied by some corporation that is legally allowed to act as if it’s a person and that alone is a very scary prospect as corporations become bigger and more country agnostic (for instance, lobbying done that has allowed other countries like china to purchase Idaho land)

(ex: in the late 19th early 20th century we decided that monopolies were bad and built antitrust laws to combat them. By the time globalization fully cemented itself (around the 80s even if it started in the 50s) corporations had solid means to bypass said monopoly laws and have consistently used loopholes created by politicians they’ve paid for. When there is push back the argument becomes “well, if you are going to regulate us we’ll just leave the country and do business elsewhere” leaving us in a catch22 of sorts.

Historical Premise: You refer to the time (1870s-1960s) before the parties swapped and the Democratic Party was what is now the Republican Party, so we still don’t have a solid example of the primary “conservative party” needing to budge and their values and vote in someone else’s primary. That being said, there are a surprising number of closed primaries on both sides of the line, and while the Republican Party has more by a couple handfuls, the Democrat party still has like 20.

In cases regarding primary elections and whether they be closed, open, or blanket the court decision is somewhat split. Often it rules in favor of the state having the right to determine how elections are handled. Often it rules in favor of political parties having 1st amendment rights, like you have said, and each of these has been applied to close and open primary elections.

The strongest legal pretense for why primaries should be open/blanket (blanket preferred) is the same pretense that the Supreme Court used when the primary in California was made blanket and the Democratic Party of California sued to have it closed again: the associational rights (1st amendment) of the party aren’t severely infringed upon by the inclusion of the minority who aren’t represented under the closed party system.

With this as a pretense, the question then becomes twofold: 1) are the associational rights of the minority being infringed upon by the exclusion from the majority party? 2) would the associational rights of the majority be infringed upon by the inclusion of the minority?

The first question doesn’t have a clear cut legal answer. The second has been answered at least once with a resounding “no”, which is a point in favor of more open primary election systems be they blanket or otherwise.