I have heard him refer to his libertarian tendencies, never the he was a (big L) member of the Libertarian Party.
Quick search yielded this>
Search> https://duckduckgo.com/?q=%22Mark+Davis%22+libertarian
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https://en.wikipedia.org/wiki/Mark_Davis_%28talk_show_host%29
“Davis describes himself as a libertarian conservative”
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http://www.libertarianrepublican.net/2010/01/libertarian-radio-talk-show-host-marc.html
“Libertarian-conservative radio talk show host Marc Davis of Dallas”
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http://letterstotheeditorblog.dallasnews.com/tag/mark-davis/
“Davis, the self-appointed media slayer of political correctness and champion of libertarian values”