As free societies, we don't "allow" them to spread anything, any more than we "allow" Indian gurus or Mayan mystics to spread their messages. The nature of free societies is openness to foreign ideas, even hostile ones like Islam, Nation of Islam, socialism, fascism, Putinism and so on. The reason the Saudis fund missionary work (dawah) so lavishly is because it (1) is part and parcel of Islam, and lack of devotion is this area (as with other spheres) would be noticed by the always angry Saudi masses and (2) is a form of exile for nutty radicals who think the royals are (a) too liberal and (b) slaves of the US.
To change the man on the street view in Saudi Arabia and other Muslim countries to a pro-US stance would require a root-and-branch extermination of their populations and their replacement by US settlers or mandatory apostasy from Islam at gunpoint and the slaughter of those who refused. Since neither of these is a realistic possibility, our best bet is sticking with our current dance partners.
Once again you are wrong. Everyone there hates us because we are best friends with the oppressive government. We are chummy with the worst evil leaders on earth, and then astounded when their beaten and crushed down people don’t seem to like us very much and call us hypocrites. It isn’t rocket science. Well. .. even rocket science isn’t really “rocket science”. But you get my point.