The poster wanted to know about the negative effects of Reconstruction, so I am answering that question.
The only direct long term negative effect of Reconstruction era policy I know of is that the South still pays exploitative railway fees to ship goods to other sections of the nation. Following the Civil War, the US was divided into 5 freight rate territories. As this book explains, the Southern territory was forced to pay the highest rate of 87% while the North paid the lowest. Many Southern railroads were purchased by Northern railroad tycoons consolidating their holdings and giving them monopolistic power to negotiate fees following the war. The railroad in Atlanta destroyed by Sherman went bankrupt 5 times in its attempts to rebuild before being purchased by the Southern Railroad, which owns much of the railroads in the South for example to this day. (These would be an example of the unpopular carpetbaggers in the question.) Although the rates were found unconstitutional in 1952, they are still in effect for the most part, since the ruling allows them to be "voluntary."
Before the war, the South was the wealthiest section of the nation and had the highest number of college graduates. The economy did not recover until the 1880s and then grew more slowly than the rest of the nation after that. The South is now the poorest section of the nation. Separating the effects of the war and Reconstruction policy to this unfortunate outcome is hotly debated, but it should be noted. My opinion is that while the war destroyed much of the wealth and status of the planter class who had invested large amounts in slaves, Reconstruction failed to improve the wealth of the lower classes very much.
Production of cotton was encouraged during Reconstruction, since cotton was vital to the Northern economy as well, while industrialization of the South may have been more helpful for it in the long-term. Here's a great paper on the topic. The share-cropping system was used to grow large amounts of cotton cheaply, but was less efficient than slave labor or if more freedmen and poor whites had owned their own land. The system eventually collapsed as mechanized farming and the Great Depression reduced the need for large numbers of farm workers leaving these workers in a very precarious position. wikipedia.org/wiki/Sharecropping Arguably much of the poverty became generational and the South still struggles with it today.
Paisley's song can be interpreted to be a little bit about the fact that the South still has not regained its economic or social status, even after 150 years, but I don't think so. I think its more about "Southern identity" in a post Civil Rights era, given that the title is "Accidental Racist," so I think the song is about race relations and the failures of the South to accept the positive elements of Reconstruction policy.