Until and unless the contradiction affects them DIRECTLY, the normies/sleepers will keep sleeping & believing the lies. The lies are comfortable because the truth, for them, is a massive 2x4 slap.

A direct contradiction would be something like a vaxxxxine injury, some trans-asshole assaulting the normie's kids, or some other direct, real-world action, that the media would then lie/coverup.

If there is no direct effect, they won't wake up.