Are you essentially saying there are no confessional, reformed, paedobaptist, congregational churches? There were in the Puritan days, correct? But they don't exist now?
The above mentioned churches, whether liberal or conservative (along with some Unitarians) are the lineal, modern American descendants of the N.E. Puritan Congregationalists.
Theologically, even Jonathan Edwards ended up a (nominal) Presbyterian, dying instantly (as it were) coming into that denomination to become president of the Theological College (later, Princeton). A true commitment to the
principles of Congregationalism means doctrinal discipline is inherently limited. Truly, Congregationalists must be more of a movement, less of an organization, when considered together. No one can tell a Congregationalist church what to believe or teach. So, "toleration" is maximized as a virtue.
However, I know a man who, many years ago and just out of Bible School, went to preach for some Congregationalists. Though professing to respect liberty of each church, a liberal rep from the local association eventually came to hear what he believed and taught (which was the Bible), and made it clear he would be removed if he stayed. So, liberalism and laxity within Congregationalism leads (naturally) to strong-arm enforcement of a ban on strict orthodoxy. If there's one thing liberals can't tolerate...