At the time of the passage of the Civil Rights Act, almost all the Senators and Congressmen from the South were Democrats. However, when it came to vote for the Civil Rights Act of 1965 almost all of the Southern Democrats voted Against the Bill and all the Southern Republicans Voted Against the Civil Rights Act of 1965.
Therefore, the opposition to Civil Rights was not a Democrat vs. Republican issue but rather a regional matter and the few in the South the did support Civil Rights were Democrats.
See the post above by Lone Ranger. That’s a long list of promoting equality and fairness.