I’m a Baptist, not a Presbyterian, and I believe Professor Boettner was correct. I began to discover the Calvinistic underpinnings of the Revolution years ago as a history major at a Southern Baptist university. As King James I said, “Presbytery agreeth with monarchy like God with the Devil.”
And a Hessian captain wrote in 1778, “Call this war by whatever name you may, only call it not an American rebellion; it is nothing more or less than a Scots-Irish Presbyterian rebellion.”
Whatever it's convenient to categorize them as in order to play up a single factor like their religion, any who remained Presbyterian after the war were far different Presbyterians with far different views on Calvinism than they were prior to it. Usually they even clearly differentiated themselves from mainstream Presbyterians from then on which is what led to a split in the US Presbyterian church in the early 1800s. A great many left the Presbyterian church and became primitive Baptists who embraced an altered form of Calvinism doctrine. They, like Calvinists, didn't believe in missionary work, the very thing the Baptist church has always considered paramount leading to a split among the Baptists due to the large number of former Presbyterians not agreeing with the Baptist mainstream.
Regards
It’s interesting you mention the Scots-Irish because by the time of the Revolution, a large number of them had become Baptists through the missionary efforts of Shubal Stearns, Daniel Marshall, and others. In fact, it was throughout the Scots-Irish regions of North Carolina, Virginia (and later West Virginia), South Carolina, and what would eventually become Kentucky and Tennessee that the Baptists became most profuse. It was among the Baptists in NC that a large part of the support for the Revolution was found - especially among those who had earlier supported the Regulator movement in the Piedmont region.