While it is true that the Republican party used to be the party of Lincoln, and that a higher percentage of Republicans voted for the 1964 civil rights bill than Democrats, modern day Republicans are very different.
In 1964 Democrats from northern states voted almost unanimously for the civil rights bill, Democrats from the south voted almost unanimously against it. The Democrats who opposed civil rights were southern conservatives, they would be Republicans today.
Strom Thurmond was a Democrat, he left the Democratic party in 1964 specifically because he opposed civil rights for blacks. Charles Pickering, the conservative judge appointed to a federal appeals court by GW Bush during a senate recess was a Democrat and switched to the Republican party in 1964, specifically because he opposed civil rights for African Americans. Many Republicans who supported civil rights became Democrats in 1964.
Look at a map of former slave states and compare it to a map of the 2004 electoral college results. Notice a pattern? Ohio, Indiana and Iowa changed from free states in 1861 to Republican states in 2004, Maryland and Delaware changed from slave states in 1861 to Democratic states in 2004. Except for those 5 states, the maps match up exactly.
2004 Electoral College Map:
1861 Slave State Map:
Not all Republicans are racist, but all racists are Republicans.