BARTLESVILLE, Okla. — T. W. Shannon will be Oklahoma’s first black senator if he wins the Republican nomination and is elected this November, but the quiet campaign stirring here about Mr. Shannon’s racial loyalties is not aimed at the African-American branch of his family tree. Mr. Shannon, whose first name is Tahrohon, is a member of the Chickasaw Nation, the most influential tribe in a state where Native Americans are not merely the inheritors of a poignant history but also collectively constitute the state’s largest nongovernment employer outside of Walmart.