This is a two part question:
What are the relationships between the 1745 Jacobite rebellion and the American Revolution? Were there any notable figures or communities involved in both conflicts? My understanding is that the American Patriots did not look particularly kindly on the Jacobite cause, even going to far as to compare Parliament's acts to Jacobitism, as seen in this political cartoon celebrating the "death" of the Stamp Act in 1766 - the skulls have the dates of the Jacobite rebellions on them. My very vague understanding of North Carolinian history also leads me to recall that the Scottish Highlander communities there tended to support the Loyalists.
Historiography: did the remembered relationship between Jacobitism and the American Revolution change over time? I'm especially curious if this is something that changed in the American South in the 19th century, especially after the Civil War.
ETA - to give an example of what I'm talking about in part 2: there is a story that the Minute Men at the Battle of Concord played "The White Cockade", which is a Jacobite tune. The story seems to come from a half-remembered recollection of a participant, recorded in the 1830s, but that began to be increasingly taken as an incontrovertible fact in later 19th-century histories, none of which explain why Congregationalist farmers of English origin would want to play a song for a Catholic Scottish pretender to the British throne.
The American Revolutionaries aligned themselves strongly with the Whig political side in Britain, against the opposing Tories. The Jacobites meanwhile had been Tories, and this contributed to a general view in England and America that Scots were all Tories. The first Scottish Prime Minister, Lord Bute, was a Tory, and New England Whigs delighted in burning effigies of him (he was often represented by an actual boot). In fact, "45," referring to the failure of the 1745 Jacobite rebellion, became a Patriot slogan after it was used by the hugely popular (in America, at least) radical Whig John Wilkes in his magazine, the North Briton. Many works written by Patriots were decidedly anti-Scottish in tone, not least the original draft of the Declaration of Independence, which called out "Scots mercenaries" for being brought in to violently subdue the English-American people. This line was deleted at the request of John Witherspoon, one of the few Scottish-born signers of the Declaration.
Viewed through this lens, it's not particularly difficult to see why the Highlanders (who had mainly settled in the Cape Fear Valley in NC, as well as a few smaller communities in Georgia and New York) for the most part took the loyalist side. They had signed an oath of allegiance to the British crown, and they'd already been through a failed rebellion against the British crown, so why would they undertake another one? Besides, the people at the forefront of this new rebellion were Whigs, and the British government was now Tory. And the Highlanders now had a fairly positive view of the British empire anyway--the historian Michael Newton has done a lot of work on this subject and found that Highlanders in the 1760s and 1770s generally viewed the Jacobite rebellion as a massive mistake, and wanted to atone for their errors by fighting for the British government. After the Battle of Moore's Creek Bridge, however, in which a Patriot militia utterly annihilated a force of loyalist Scottish Highlanders, many of them, fearful of harsh retribution, didn't want to fight and simply tried to stay out of it. A large number would emigrate to Nova Scotia, and a few, such as Flora MacDonald and her husband Allan, even went back to Scotland.
One interesting story I've heard was that the main church in the Highland settlement in what is now Fayetteville, NC, was co-ministered by two men from the Highlands named James Campbell and John McLeod. Campbell was the senior minister, from Campbeltown in Argyll, while the younger McLeod came from Skye. Campbell was forced to leave his congregation after he was apparently threatened after praying in support of the Patriot cause, after which McLeod, a loyalist, became the only minister.
While most ex-Jacobites tended to have a loyalist outlook, there are a few examples of them fighting for the Patriots. The most notable is easily Hugh Mercer, who was from northeastern Aberdeenshire (meaning that he was probably not a Gaelic speaker) and became a close personal friend of George Washington, and a Brigadier General in the American Revolution (he was killed at the Battle of Princeton in 1777).
I don't really know why "The White Cockade" would have been played by the Patriots, particularly if it was by a New England regiment. Perhaps they just liked the tune.
With regards to your second question, I think the 19th century romanticization of the Jacobites and Highland culture in general essentially triggered the more positive reaction and willingness to draw parallels between that rebellion and the American Revolution (which ironically never existed). I've talked a little more about that, and more specifically the relationship to the Confederacy in the Civil War here.
For more on this topic I'd recommend Duane Meyer's book The Highland Scots of North Carolina. I'm pretty sure that free PDFs of this can be found online.