It's a simple fact that SpaceX chose its CEO's public image over its mission statement and reputation. I hope future prospects realize that there is no stability or long-term personal growth to be found there unless they can keep their heads down and kiss ass.
But if they can't work anymore because they got fired from the one employer of their skill the consequences are quite severe. They have to learn a new field! Ideally I'd say people with this specialized skill set form a guild or union. The same thing that makes them vulnerable makes their employer vulnerable--the workers of that industry are highly concentrated, with high investment in skill development. Absent that, it's a tricky issue and I think it would be fair to say that at least a warning would have been in order before dismissal.
I don't know if the people Musk fired are in this category or not. If it were an office manager, for example, seems fine. if it is an engineer on some space ship esoterica, ouch.
Perhaps this isn't a good analogy, but if you yelling insults at the the neighbors makes it harder for him to fix the toilet, and he asks you to stop, would you still fire him for it?
Because you could argue, although with difficulty, that Musk tweeting stupid things makes it more difficult for SpaceX employees to do their work.
In practice, I've found it generally easier and wiser to leave a company with a stupid boss rather than ask the stupid boss to change, but I see why someone could try the latter.
Your point is a good one though, to continue the analogy, the plumber shouldn't want to come back. Erratic and volatile bosses are best avoided. I prefer it when they do this stuff loudly and in public so I can know to avoid them.
Also I am not threatening his career, he is, he is choosing to take a principled stand and should understand the likely consequences and be willing to accept them.