There was no point in running as a Republican in Texas, or in the rest of the South for that matter. A Republican couldn’t get elected to the Library Board. The Democrats were certainly the Segregationists, but they were also the Communists. Strange bunch, even back then.
Well, running for statewide office as a Republican was a fool’s errand. Federal was a different story as there were breakthroughs, as Republican John Tower won LBJ’s Senate seat in 1961 over Tory Democrat Dollar Bill Blakley and GOPer Bruce Alger had been the Dallas County Congressman since 1955 (but lost a decade later in the wake of the assassination when he was explicitly targeted for defeat and blamed for “fomenting right-wing hate” against JFK there).