Here is my take on the changes to civilian society in both North and South brought by the outcome of the American War of 1861-1865.
The entire nation was set upon a course to industrialization. The family farm was set upon a course to destruction because people are more valuable to industry if they are standing in line at the factory door begging for a job, (The more people who seek jobs, the lower are the wages that the factory must pay.) than if they are making a living by themselves on a farm. (I speak of farming for family subsistance.) Thus has evolved a body of regulations and tax structures that make the family farm unprofitable. Farms, to be approved of by our industrial and corporate managers must be producing for market needs. Production for family subsistance is not allowed. Hence the reason that so much good land is idle in the United States, land on which individual families could be leading a superior (though not wealthy) life-style.
And what of the small businessman? The small businessman has fared better under industrialization and corporate big business than the subsistance farmer. This is because the small businessman is the most productive segment of society, and the taxes paid by small business are drawn upon to subsidize corporate big business. Thus, small business is allowed to survive to the extent that it is needed for a tax farm. Big business has never been content to survive on its own earnings; it has always sought to transfer wealth created by other segments of society into its own pockets; that is what, in my opinion, distinguishes capitalism from private enterprise. If the small business sector gets too big relative to the need it fulfills as a tax farm, tax structures and regulations beat it down, so that those small business employees excess to the need are forced into the job line at the factory door.
I would say that the most evident difference in the South was the absence of slavery. This would have to be one of the most fundamental changes that Southerners had to address. The institution of slavery, its codified premise of wealth, and the social rigidity that it offered were all abolished after the Civil War. Certainly, new measures such as restrictive laws that pushed segregation were adopted, but there was a transition period where the freed Black person was a major change to Southern society. In the North, the great migration was another social change, where Blacks from the South came to the North. Both forces of change brought to light the discussions of thinkers like Wells, Washington, and Du Bois which centered on how the Black individual in this setting would fare and what path they would take. The massive industrialization that helped bring the North to victory began to extend to the South, which began to adopt the principles of Northern industry in its own territory. The lifestyle change from agrarian based South to a domain driven by industry also prompted a change in civilian society.
It's a very broad question, but I can get you started. Civilians in the South after the Civil War suffered through a prolonged time of economic difficulty, so there were strains on both families and individuals trying to get by in southern communities. To make matters worse, 1/5 of the South's white males of military age were dead, leaving a gaping hole in their society for a generation. Slaves had been freed, but the war did little to change the majority of peoples' opinions on race.
In the North, the cities had grown as the industry supporting the war got up and running. There was a sense of opportunity among common people, but it was largely an illusion and unrealized during the Gilded Age. Many if not most in the north were still racist against blacks and immigrants. 2 million veterans came home, some of them damaged physically, some damaged mentally by what they had seen and done. The population growth that had started in the north in the early 1800s continued, and in fact, gained momentum.