SpaceX did not immediately respond to a Reuters request for comment.
The New York Times reported on Thursday that SpaceX had fired employees associated with the letter, citing three employees with knowledge of the situation.
It had not detailed the number of employees who had been terminated.
Reuters could not independently confirm that report.
Billionaire Musk is pursuing a $44bn bid for Twitter and has made clear his support of freer controls on speech on the site.
Musk, also head of the electric automaker Tesla Inc, has been in the headlines and featured in late-night comedy monologues in recent months, including over his quest to take over Twitter, his criticism of Democrats and a reported allegation of sexual harassment, which Musk has denied in a Twitter post.
Founded by Musk in 2002, SpaceX has played a central role in the recent US space program.
