Pennsylvania and Rhode Island were not bound together by "common religion" in the sectarian sense, but by a covenantal understanding of community that went beyond religious sectarianism. William Penn and Roger Williams were explicit about that. That's why so many Jews settled in Philadelphia, they had no laws persecuting Jews, and in the early years, much of Washington's army was bankrolled by Jewish moneylenders, some of whom lost everything financially backing the revolution.
The Quakers and Baptists were motivated by a distinctly Protestant Dissenter impulse, first articulated by Sebastian Castellio, that the true elect of God must reject using violence to coerce people into the correct doctrine, that love, not violence, was the basic grammar of reality, of the Kingdom. John Locke actually was deriving his ideas on religious freedom from thinkers like Hugo Grotius and Castellio before him, they didn't come out of nowhere.
What probably needs to be reclaimed is the sense of common good and basic natural law ideas that humanity exists in an implicit covenantal relationship with one another, that we aren't isolated individuals, not specific enshrining of sectarianism as normative, which will do no good and isn't consistent with the deepest impulses of the Christian tradition (going all the way back to at least Martin of Tours's critique of violence as the logic of the emerging Christendom).