I knew he ran as a Democrat-in-name-only (just as in many parts of the country people desiring political office due to get elected - maybe less so today.)
In fact, that was what much of the Sourh politicians were: Dixiecrats and many became Republicans just prior to and especially after he was elected, the candidacy of my beloved President Ronald Reagan, who had been an early Democrat but stated "the party left me."
A few in the South, perhaps, but many were diehard Democrats (I grew up here, so I know) and died as such. I’ll give one example I mentioned the other day. Former Alabama Governor John Patterson (who served from 1959-63). He ran as the Klan candidate in 1958 and defeated George Wallace (Wallace was NOT a segregationist in that race). He got close to the Kennedys. 50 years later in 2008, ex-Gov. Patterson endorsed Obama for President.
As you can see, some were just fine with the Democrat party of yore as they are with it today.