Statistics literacy would help, but there are a lot of highly educated people who repeat things like the pay gap myth. I think the problem is more about ideology and the lack of critical thought.
If even PhD's can't be expected to adhere to basic standards of intellectual honesty and critical thinking, then how can we ever expect the general society to grow up and realize the value of these things? How can we, the enlightened few (I say this half-seriously, of course, because obviously I am not without fault myself), ever expect to be able to lead a logical conversation with most normal folks we encounter in our daily lives, even with our parents, spouses and children? Seriously, most of us will never be able to choose their spouse from that tiny minority that understands honest and logical discussion. They will have to settle for something less. Most of us will have children who will never understand what we understand, simply because the school, the society and even our spouses will teach them to act based on emotions and false values. Basically, we are doomed to be eternally dissatisfied with the way our lives turn out to be!
I have to admit, conversations about critical thought in society invariably make me depressed.
I've met several people who treat my tendency to value critical thought as if it's nothing more than a quirky personality trait, and acting based on emotions and feelings is just as valid. It's infuriating.
I tend to focus on intellectual integrity in argumentation. But when I talk to most people about "intellectual integrity" or "intellectual honesty", I think that they tune me out. Those terms don't really register.