The groups you mention, Baptists and Congregationalists, had in common the congregational governance of their churches. There was no clerical connection between churches, each church called their own pastors and conducted their own business with all members participating.

What has changed, at least among the Baptists, is the influence of a futurist interpretation of Biblical Eschatology, or end-times views, known as Premillenial Dispensationalism. It attempts to use the Bible to try and apply modern events to a timeline that ushers in the "rapture" or literal resurrection of the church, the millenial reign of Christ, a literal "tribulation" and the return of Jesus. Dominionism is tied to it.

It's a gross misinterpretation of the Bible, requiring a way of looking at it that goes way outside the boundaries of its historical context. And it has an effect on the church's "worldview" with regard to its role in ushering in the second coming.