Republicans – Moderate and Liberal Republicans supported civil rights. The Republicans who supported civil rights in America were not conservatives of the same ilk as George W. Bush, Rush Limbaugh and Glenn Beck. They were liberals and moderates, people like former Rhode Island senator Lincoln Chaffee and former senator governor Nelson Rockefeller.
Conservative Democrats opposed civil rights. The Democrats opposed to the civil rights movement weren’t Democrats with the center-left ideology of Bill Clinton and Barack Obama. They were, in fact, conservatives – especially from the south – with far more in common with Limbaugh, Beck, etc. than any modern mainstream Democrat. When people say that someone like notorious segregationist Bull Connor was a Democrat, they are technically right on the party label, but when it comes to ideology Connor and the rest of those opposed to racial integration were conservatives.