You don't reconcile with Confederates any more than you would "reconcile" with the Third Reich. And, I mean, Wilson was definitely on the slaver side. And no no, we know who is still on the side of evil. It's the people who defend monuments to the Confederacy and Southerners who vote Republican.
"The Solid South" was the term, in case you forgot. The former Confederate states full of white conservatives who voted Democrat no matter what, because they wouldn't vote for the party of Lincoln. Until, of course, 1964. Now, what was it that happened in 1964, that caused all these pro-slavery racist monsters to switch, en masse, to the Republican party? What made the former Confederacy, previously "solid" for Democrats, to become equally as solid for Republicans? Oh yeah, it was the Civil Rights Act of 1964, followed by Barry Goldwater's presidential run, which he predicated on opposition to the CRA.
And so, boom. There you have it. Conservatives have been pro-Confederacy and pro-slavery since forever. And continue to be on the side of the mass-murdering, slaving traitors to this day. As evidenced by both your comment and others.