Not entirely true, I think. Doesn't she support leaving the police and military in state hands?
Anyway, I might expand on this later, but the "cult of Ayn Rand" treats her as some groundbreaking philosopher who supposedly proved that "a free market is a corollary of a free mind".
Readers are presented with some premises vague enough to be valid (i.e. reason is good, A is A") right next to poorly thought out arguments. The greatest irony is that she drones on about the existence of an objective external reality, and then goes on to ignore material conditions in her version of human history, in which a few individuals "choose" to exercise reason, setting them apart from the so-called "human ballast" (i.e. "unskilled labourers"). She compares these individuals to Atlas, who you may know is the god in Greek mythology who was said to hold up the globe. Rand directly targets alienated bourgeois or petty bourgeois individuals and calls on them to use their reason to innovate and get ahead in a capitalist market---in short, to spend their lives with the sole, cold, restless purpose of the selfish pursuit of advantage in a capitalist market (to be the proverbial "Atlas"es).
In short, its cultish because it encourages (ironically) the stunting of reason, and an endless pursuit of some divine status as a capitalist titan. When you treat selfishness as a virtue as she does, you'll perpetually disappoint yourself until you can convince yourself that you got where you are in life all on your own, in spite of, rather than because of, association with other people.