They mash both buttons. Cognitive dissonance is basically just entry music for self-styled "liberals" today.
For reference:
lib·er·al
adjective
willing to respect or accept behavior or opinions different from one's own; open to new ideas.
OR
big·ot
noun
a person who is obstinately or unreasonably attached to a belief, opinion, or faction, especially one who is prejudiced against or antagonistic toward a person or people on the basis of their membership of a particular group.
I'd say calling themselves 'liberal' is a misnomer. You be the judge.