There are a number of open court cases on if he can fire people like that. There are some injections in place already, and the supreme court is likely to get involved. It isn't clear if Musk's job is even legally something he can hire someone for. All of this will take years to work out in the courts and so there won't be repercussions for a while.

The above is really complex. I don't pretend to understand the laws.