A bit of a tangential question, but one I know a little about. Mostly correct, but I'd phrase it differently: up until the civil war, the Republicans were generally left-leaning and Democrats were generally right-leaning.

In terms of what lead to the switch, after the civil war, there weren't a whole lot of politicians in the south from either party who supported abolition. A solid number of those politicians likely saw a need to work together if they wanted white supremacy to succeed in a nation that just rejected their racist bs so hard that they fought and won a war with them over it.

Initially, the Democratic party was to remain the bastion of right wing regressivism, but the lines weren't firmly established until democrats started voicing their support for civil rights. Most majorly, Truman voicing his support for civil rights began the redrawing of the lines, and LBJ passing the civil rights act cemented the switch. All remaining Democrats who opposed civil rights switched to the Republican party, where they would cultivate and appeal to voters who shared their opinion on civil rights by developing and implementing the southern strategy.

This is the foundation of the modern Republican party - they were the party formed to oppose and undermine civil rights, a role they've maintained to this day.