Of course, they don't have to provide equitable treatment to candidates in other ways.
What is the state or federal government interest in how a private organization chooses to endorse a slate of candidates? Will we see lawsuits and government regulations over how the Sierra Club or NRA choose to endorse candidates? Will we see state officials stepping in to run or monitor caucuses or conventions if the state party decides to do that instead of a primary?
Just because a party primary has the same mechanics as a general election, that doesn't necessarily mean it has the same legal status--or that it should. In fact it's arguable that spending state resources to help a group of private citizens decide who to endorse is an example of straight-up corruption and waste of taxpayer money.