White's church ties will pose no problems for Texas Democrats if they have to choose between Andrew White and Greg Abbott.
I looked at his campaign website, and I'd say he is more liberal that folks Texans have been electing statewide. He tries to be careful in his position statements to "thread the needle" -- e.g. "In my personal life, I accept that life begins at conception" but "I support Roe v Wade." Being the son of a former governor is in the "helpful" column for White (though I not sure just how popular Mark White was -- he defeated Bill Clements, then was defeated by Clements). The elder White was born in our county, and the "Wells" in his middle name represents a once-influential family in the earlier days of the county.