He's expressed support on the "right" of businesses to discriminate based on race/gender/etc[1]. As well as libertarianism being critical of the civil rights act, the civil war, etc [2].

How is that doublethink?

[1] http://www.cato-unbound.org/2009/04/13/peter-thiel/education... [2] http://reason.com/archives/2010/06/16/racism-civil-rights-an...