Except Lincoln's last speech mentioned giving Freedmen the vote in certain cases.
He'd manage to chart a middle course, giving the Freedmen their 40 acres, maybe pushing for a homeland of sorts for them - there might be le4ss than 50,000 go to New Mexico but I think Lincoln pushes for this and maybe some of the land the Exodusters later pushed for OTL, as they settled in Western Kansas and places like that. Perhaps Colorado gets a large number of blacks, too, or Wyoming/Montana.
Lincoln pushes for an end to the Black Codes in exchagne for some states being allowed in quickly, as noted, and so Jim Crow exists, but in certain states, the plight of the Freedmen is greatly enhanced; Louisiana for one was a place where they were trying to develop under the German (I think even German-born) governor for a while. Tennessee, too, could have that.
So, Lincoln might well encourage these states as "noble experiments," while focusing on blacks trying to get into areas such as sports - my 2 AH POD books might see something slightly different but still very similar to thsoe TLs. Lincoln liked baseball OTl and reportedly was lpaying it when informed of his nomination, before they had pro teams.
So, the turn of the century woudl see a patchwork of places even int he South which were much clsoer to the North (like Louisiana and Tennessee), places in the North which are starting to see integration (New York City police, IIRC, had their first black patrolman around this time, it hink baseball could remain integrated with a limit like the NFL had of 2 per team for a while). Essentially, Lincoln woudl be seen as charting a middle of the road course even after his Presidency that saw thigns not as good as they could ahve been, but not as bad in some areas, either.