The original study was flawed  (understatement) and said the opposite.

…the American Journal of Political Science … published a finding much beloved of liberals a few years back that purported to find scientific evidence that conservatives are more likely to exhibit traits associated with psychoticism, such as authoritarianism and tough-mindedness, and that the supposed “authoritarian” personality of conservatives might even have a genetic basis

Oops

The authors regret that there is an error in the published version of “Correlation not Causation: The Relationship between Personality Traits and Political Ideologies” American Journal of Political Science 56 (1), 34–51. The interpretation of the coding of the political attitude items in the descriptive and preliminary analyses portion of the manuscript was exactly reversed.

Read the whole article.