A good chunk of modern Protestant movements are more a rejection of the High Church crowd than a rejection of Rome.
Which makes me wonder, seriously, why does the Catholic hierarchy think it useful to drag in a half a dozen Anglican congregations while there are gazillions of Methodists out there who'd take half the effort to bring into that particular fold?
Is it the class system at work or what?
I don’t see much of a connection between Rome and Methodism.
Methodism and the Oxford Movement had similar roots in a protest against the CofE’s moribund faith in the aftermath of the Glorious Revolution of 1689 if I recall directly.