If the CEO makes it harder to land contracts or recruit talent, that's a direct impact to working conditions. I loved SpaceX and would consider working there if not for Musk, for instance.
FWIW, I think firing the organizers is an overreaction and that it would be in SpaceX's best interest to muzzle Elon, but it's hard to conjure up a legal argument that they can't do it. And you'll notice that the company's statement said nothing about the content of the letter, only that it's inappropriate to organize it with company resources and on company time.
Knowing that people like you with your reasons for not working there are not present and harassing people towards your view point could be a recruitment draw no?