How does one avoid the propaganda? Ultimately you can't.
Let me give you a personal example.
I do not celebrate Christmas for religious reasons. But even though I do not, it so permeates the culture that one cannot avoid it. My daughter does not celebrate it either, but yet, many years ago, she was convinced Santa Claus existed. Where did she get this? Not from me but from the culture around her.
While Babylon cannot be avoided entirely, you can reduce your exposure to it. One way is to seek out opinions with which you disagree. In other words if you are a conservative, watch MSNBC; if you are a liberal watch Fox News. You need to hear things that annoy you. An echo chamber only leads to intellectual inbreeding. You need to understand that the techniques of propaganda are used by both the right and left heads of Babylon the Great. Yes, I am saying that both are ultimately the same, both servants of the same master. Watch nothing without a critical eye and a lifted eyebrow.
If you want a more detailed look at Edward Bernays, be sure to look
at this multi-part series by Pam Dewey, the beloved Editor of the Prophecy Podcast blog.