Preventing employer retaliation for discussing the conditions of employment are a pretty significant part of the protections around unions. An open letter discussing the conduct of the CEO falls under discussion of the conditions of employment.
There are limits to what companies can do to try and prevent unions from forming. SpaceX is claiming that those restrictions and the way in which they're enforced by the NLRB are unconstitutional. Seems pretty fair to characterize that as something which would bust up some federal union protections.
You're right about the outcome SpaceX is seeking. But the critical thing you're missing is the argument they are making against NLRB. The legal arguments aren't really about the specific facts of the case but, rather, about constitutional issues that go to the heart of how NLRB adjudicates labor disputes. From the article:
> It claims the NLRB’s proceedings, which involve a hearing in front of an NLRB administrative law judge (ALJ), violate SpaceX’s “constitutional right to trial by jury.” The company also accuses NLRB of violating the Constitution’s rules on the separation of powers, stating the agency’s structure “is miles away from the traditional understanding” of the concept.
> Why should companies be forced to employ people who actively work to harm the reputation of said company?
The irony being that the content of the letter is in regards to Elon Musk's work to actively harm the reputation of said company. By this token, why should employees be forced to work under petulant, capricious, myopic executives who undermine the efforts of the people with boots on the ground who do all the actual work?
Sounds like a strong case. Why should companies be forced to employ people who actively work to harm the reputation of said company?