The Scots-Irish are largely the descendants of Lowland Scots who migrated to Northern Ireland in the 16th and 17th Centuries under the Tudor and Stuart dynasties in an attempt to establish a Protestant presence in what had been the most strongly anti-English area of Ireland. There is some mixture with Highland Scots, northern English, "native" Irish, and a few French, Flemings, and Germans, but the Lowland Scots element is predominant.
The Lowland/Highland split is one between Germanic Anglians (including Anglicized Picts and Britons) and Celtic Gaels, whose remote forbears originated in Ireland, though with considerable Viking and Norman mixture. Despite their cultural and linguistic differences, both Highlanders and Lowlanders were predominantly Calvinist by the time of their migrations to America. Whether Lowlander, Highlander, or Scots-Irish, their concepts of liberty of conscience and the duties of rulers to be subject to law strongly impacted the formation of this republic.
The Law is God - I think that was their motto (I could be wrong - maybe that was Cromwell?)
I didn't know that the majority of Highlanders were Calvinistic by that time.
I have a great admiration for the Scottish political tradition. I think the Scottish managed to do what the French failed to do in their respective Enlightenment contribution - justify their classical liberalism via their Christian faith. Perhaps that is because France drove its Calvinists out and ran an anti-clerical revolution?