Shortly after Douglass delivered that speech, several Southern states enacted laws that placed severe legal restrictions on the rights of blacks Wickham distorts. There was no "shortly" about it. For the next ten years Reconstruction, sponsored by the Republicans, kept blacks free. Democrats demanded an end to Reconstruction as the price to end the consititutional crisis after the election of 1876. Only after the end of Reconstruction were southern Democrats free to enact the Jim Crow laws. The South thereafter voted reliably Democratic until after WWII.
During the period between Douglass' speech in April 1865 and when Congress convened in December 1865, the Southern states passed the so-called Black Codes, which conceded some basic rights to black people, but severely restricted their economic and civil rights; the point was to keep the freedmen as a pool of cheap labor working for whites and not economically independent. The North saw this as an attempt to restore slavery under another name, and Congress (then heavily Republican) passed the Civil Rights Act of 1866 and what became the 14th amendment (when ratified by sufficient states) in order to prevent the enforcement of the Black Codes.
The later Jim Crow laws were not as bad as the Black Codes. Under Jim Crow, black children had to attend separate schools; the Southern Democrats right after the war didn't believe in any education for black people.