Most Irish in the South were Scots-Irish or Prod Irish and came quite early like you said.
They were not enamoured with their kin who came later and were mostly Catholic.
That stock is arguably the majority of my DNA btw.
These days many descendants of such Irish prefer to be known as Scots-Irish ~ but they're not!
There are a number of reasons why the Catholic church wasn't very well organized in the United States in that period (1800 to 1854), but most of it gets down to the fact that there simply weren't very many Catholics to "organize"! Newcomers were on their own. The Baptists were in strength and welcomed then with open arms (as did 9 synods of Lutherans, etc).