It's not a question of propaganda, the issue is rather how you identify propaganda for what it really is, how you learn facing it. And having the choice between multiple authority figures is fundamental for a balanced psychological development, and for the developement of critical reasoning. Paradoxally, public schools are vital should you want to understand the need to challenge authority sometimes, and why. When you first learn to challenge your teacher or the other pupils, you learn this lesson.
With homeschooling, you don't have this choice, since you can only trust one source of authority: your parents. And even with the best parents in the world, this is a very dangerous situation. Homeschooling is most of the time a pretense for parents who want to keep a total control over their children, who are unable or afraid to delegate their authority.