"In Boston one has to be something, and Unitarian is the least you can be."
Unitarianism by the 20th century didn't have any dogma, even atheists and agnostics could be members, and accepted that all religious traditions had spiritual wisdom to offer. But because it had evolved from Christianity it had institutional legitimacy, in a world where church membership was a social requirement.
People's beliefs might have changed less than we think over time, despite the common perception that nearly everyone in the US was hyper-religious until the last few decades.
There might be other factors around the decline in church membership -- perhaps related to the decline in participation in secular community groups as well.