What is it?
Congregationalist polity can (though not necessarily) serve to encourage both liberal and conservative communities to see themselves as the still centre of religious authority and so, without reference to wider contexts, able completely to shape their communities according their own current personal prejudices (beliefs). The trouble with this polity is that it has a tendency to develop in rather sectarian ways - indeed the history of Protestantism shows an endless proliferation of conventicles and sects with each group becoming increasingly and dangerously self-referential as it closes down its boundaries.
Not surprisingly non-Congregationalist traditions readily point to this fault and use it to justify their commitment to some kind of institutional authority (Presbyterian, Episcopal or whatever).
Related
References
Brown, Andrew James. “Garden Congregationalism.” Caute, 7 Aug. 2008, https://andrewjbrown.blogspot.com/2008/08/garden-congregationalism.html.