Will the average person only preach equality while secretly understanding reality? No, because the best liars are the ones that believe their own nonsense. Humans internalize their societal taboos and stick only to what is proper to say, act upon and yes, even think.
That’s at least true under normal circumstances. But now imagine you took an average liberal and told him that you had 100% irrefutable evidence about whether there were genetic racial differences in IQ. You put a gun to his head and ask him whether HBD is true and tell him if he guesses wrong you’re going to kill him. At that point our liberal might start dispassionately weighing the evidence. But until that point comes or his car breaks down in a black neighborhood he will lie to others and himself. An abstract interest in truth for its own sake is a rare eccentricity.