The left has a lot of criticism of Lincoln and the Republicans for not being woke and anti-racist enough. Historically, too, there was much criticism of Lincoln and his party for being capitalists.
For a long time, Democrats felt much attachment for Jefferson, Jackson, and the Southern roots of their party. They don't anymore, but much of what they say about Lincoln is an effort to appeal to Northerners who grew up thinking highly of Lincoln. There's always been at least a little ambivalence about Lincoln, his party and his army, though. So no, it's not approval without qualification.
I don't know about today's Southerners hating the US of the Civil War period either. Not everybody is as in to the Civil War as people on this thread are, and a lot has changed in recent decades.
I’m not speaking of FR only. I’m speaking all my life living in a Dem stronghold how much the regular Dems love Lincoln. That ambivalence is literally like the last year, as BLM realized no white is good enough. I don’t count the last year, I count what I saw over decades living with commies who worship him while despising and ignoring Washington; history books, historians and politicians opining on documentaries. That is my Gods honest observation.