Ayn Rand said that of all the things public funds were ever spent on (outside of judicial and national defense), NASA was the most worthy. She wrote admiringly about NASA, revealing a deep respect for its technology, scientific pursuit, and its Apollo launches. They even specifically invited her to an Apollo launch.
I don't think someone that hated NASA - or supposedly would dislike a private SpaceX - would write: "Apollo 11: A Symbol of Man's Greatness." Clearly since Ayn liked NASA, she would love SpaceX as a step in the right direction over public space exploration.