At How Democrats and Republicans 'switched sides' on civil rights | Death and Taxes Robyn Pennacchia says,
"From 1860 on, republicans were pretty concerned with backing away from the whole "rights for black people" thing because they didn't want to "alienate" racist white people. Basically, during the last half of the 1800s, everyone was racist and no one was the party of civil rights.

Teddy Roosevelt was President William McKinley's veep, and a progressive Republican. After McKinley was assassinated, establishment Republicans hated his guts which further alienated the conservatives in the South.

Then came Herbert Hoover, a republican who ran against New York governor Alfred E. Smith, a catholic democrat. Hoover recruited some KKK members and they got everyone in the South freaked out about the possibility of a Catholic in the oval office.

By the time Franklin Roosevelt took office and created the Fair Employment Practices Committee. Most black people started voting democrat for dislike of Hoover and respect for FDR.

When Barry Goldwater became the Republican Candidate in 1964, the southern conservative democrats embraced him because he voted against the Civil Rights Act and was way more conservative than previous republicans. They started to turn republican.

Nixon used the fear of hippies and commies and radical black people to woo the southern states again.

Then Regan embraced the Religious Right and opposes "Welfare Queens" a dog-whistle term for poor black single Moms.

The southern conservatives are now solidly republican and blacks are democratic.

Today, catholics, hippies, commies and blacks are not a threat, but Donald Trump has used that fear of people who are "different", Mexicans and Muslims to rally the conservatives again.

Links:
How Democrats and Republicans 'switched sides' on civil rights | Death and Taxes
Political Polarization
Conservative Christians and Republicans