It is true that high church/low church refers to the style of service, and I alluded to that, if you read back, the denominations included in high church, as opposed to those in low church.
But, in the South, the phrase went beyond Anglicanism, as Episcopalianism quickly became a religion of the affluent. Prior to the WBTS, the South as a whole had less religious division than the North. There were prosperous Jewish communities in most of the major Southern cities, there were no Jewish ghettoes though. The South in general, showed a greater religious cooperation than did the North. The war ended that. In general, in the South, Catholicism was very much an elite religion, or at the very least, it didn’t contain the connotations of poverty that it did in say, Chicago or New York. The South took religious cues from Maryland in that regard. Catholic immigrants didn’t begin arriving until the 1840’s-50’s, and so by in large, the Catholic tradition was a colonial tradition, and so, Catholics were part of the establishment along with the other religions.
Reconstruction ended when the Bourbons took back power. The Populists rose in the late 1880’s, and they mixed religion and politics, and they noted that in general, some faiths tended to have members of a better standard of living than did others. So, populist politicians who also incorporated religion into their approach openly derided “high church elites” as holding the poor man down. And they had a point, from the end of Reconstruction to WWII, what they were saying was true, in general, there were class disparities in religious preference, and many politicians exploited this successfully to the detriment of the region as a whole.
Then again, this is more of a region specific, and state specific thing, specifically, the gulf states is where this was real prevalent. But, you still do see the pattern today, to a degree, with some obvious examples, and then some less so, though demographic changes have begun to alter this.