Most Liberal:Rhode Island/NY GOP
Most Conservative:OK/ARKANSAS DEMS
Oklahoma is clearly has the most Conservative Democratic party, I mean just look at the rage voting against Obama and random candidates getting high % this year. Fun fact, many Hawaii Conservatives are registered/elected as Democrats do to the Republicans having no electoral power.
Yes on Hawaii, No on Oklahoma (old-style conservative Democrats are mostly substituted by Republicans now, and Democratic faction became much more urban and slightly more liberal as of late), may be - on Arkansas (though the same process is going on there as well, and old-style conservative Democrats are more and more substituted by Republicans now, and Democratic party becomes "black and urban" party now...
Oklahoma could be the answer- a pro-life advocate who switched to the Democratic Party to run against Obama in the 2012 primary won several counties in the state!