It's worth noting in this context that the current system of government-funded science, which seems normal, in fact was invented more or less single-handedly by Vannevar Bush shortly after World War II. [1] The scenario that worries you was the norm for approximately the previous history of humanity. (This isn't to say governments never funded science, just that they didn't dominate it as the US Government does today.)
Will these patrons support academic freedom? An organization that challenges the social order? What if your research upsets someone; is your career/organization at risk? Will their ideas and whims serve the nation and world?
Every one of these questions applies with equal or greater force to government-funded science. Anyone worried that a private patron of science might, e.g., put his career at risk, should be a thousand times more afraid of the Feds.