As one of the mainline churches in the US the Methodist church has been influential throughout America's history. What if this mainline church became the majority denomination of the US? It doesn't have the official state religion but come up with a timeline that sees the Methodist Church as the 'American Church'.
That was actually how things were going to go in the immediate aftermath of the American Revolution - despite religious pluralism and all that, Methodism was the fastest growing denomination even in Colonial America. (Hence part of the reason the Protestant Episcopal Church, as it was then called - to differentiate from the Methodist Episcopal Church (hence the AME and AMEZ churches) - was formed as a survival mechanism for Anglican congregations in the US who did not want to go that way, by way of the Scottish Episcopal Church and its peculiar views as a result of the Jacobite Wars.) It's perfectly conceivable to have Methodism not only be the majority denomination in that case, but even as a de facto state church from the beginning of the Revolution, in that case - with very little alteration to OTL.