If you presented people with a Red Pill/Blue Pill choice there is a very good chance that they would not believe you. Certainly, in the movie, NEO has some impossible things happen, which open his mind to the situation. However, what would be the trigger for a normally asleep person to realise an alternative exists.

At the moment we hear the new term "Fake News". Do people question the "Real News"?

As used by Jonathan Swift - "There are none so blind as those who will not see. The most deluded people are those who choose to ignore what they already know."