Who is the most liberal Republican governor?

Not sure but Western states governors tend to be to the right of the Democrat mainstream such as Bill Ritter of CO, Brian Schweitzer of MT. Also there are Southern democratic governors such as Phil Bredsen of TN, Mike Easley of NC, and Mike Beebe of AR, Steve Beshear of KY and so on... Also in 2007, Mississippi held its gubernatorial election, Republican incumbent Haley Barbour vs. conservative Democrat John Arthur Eaves, Jr. Even though it was a longshot, Eaves (who sounded like a moderate Republican minus the economic stances) lost. However if elected, due to his stance on the issues, Eaves would have been the most conservative Democratic governor in the nation. Hope this helped.