By decreasing their standard of living.
How does a tariff hurt a subsistence farmer in the South more than it does one in the North?
See above.
When the topic is the socioeconomic makeup of the South, we hear that the vast majority of the population was dirt farmers with no stake in slavery.
Much of the North, South and the rest of the world depended on slavery.
When the Confederate army is discussed we hear that almost all reb soldiers were not slave owners.
True.
Yet when the tariff is discussed, "the South" becomes a land that was 100% populated with plantation owners growing cash crops who would be hurt by a tariff.
Wrong. Economics is not a difficult subject.
By decreasing their standard of living.
I may be wrong, but I believe that by definition a subsistence farmer, which much of the country was in 1860, is pretty well insulated from the market. Especially in the cash poor South. There would a small investment in the simple farm equipment of the day, but he's not going to buy many manufactured goods, especially from the North. They grew their own food, produced their own clothing, but had no stake one way or the other over the economic issues that concerned the cash crop producers. I've seen a copy of my North Georgia great great great grandfathers' will of 1859 and there's not much there that wasn't produced locally.