It's hard to imagine how the US could ever have managed an independence movement without the ideology of Protestantism as an organizing framework. And Haiti only managed it because of the successful example of the French Revolution, so that model would have been out too.

There was so much input from Protestant church music into the music of the slaves in the US that that would have been very different.

I presume all of white America would be dancing to something like Cajun.

If Britain had developed into a centralized royalist state, local aristocracy and gentry would have had far less power, so there would have been less clan rivalries to compose ballads about. (I don't think there any ballads like Chevy Chase in French tradition, are there? Hardly any in Ireland either).