But ultimately, the south fought a civil war in order to preserve the institution of slavery because it was the fundamental organization of society on top of which the economy was built, and many non-elite white men nevertheless allied themselves with this effort.
As for projecting the past, I don't know. It's certainly plausible that White people today are still reaping the benefits that were established by slavery and racism in a broad, systemic sense. As far as I know, my relatives didn't own slaves, but my relatives did do things like get mortgages that Black people couldn't do. That doesn't seem fair does it? It's a little bit like inheriting stolen property. But if you go back far enough, what isn't stolen property?
Which states? This is easier to imagine of e.g. South Carolina than of Tennessee.
In general, exaggerating differences in the interests of different portions of the working class is not to the advantage of the working class. American blacks have suffered more from our racist authoritarian capitalist system than poor whites have, but they have both suffered. Many residents of southern states did not enthusiastically join the war effort; this was why they had to have a "Confederate Home Guard" to brutalize conscripts.
Upthread you claimed that such small farmers also used slaves. That may have happened occasionally, but the basic requirements of agriculture in a temperate climate (there is a limited time period during which particular tasks can possibly take place) would have made it rare.
Regardless, offices again had property and tax qualifications in virtually all states.
Not to mention that the target of those laws were, now considered white, immigrants rather than the always minority blacks in the north.