The post-bellum period in 19th century America saw the rise of several important strands of religious liberalism. For Unitarian-Universalists, the most significant is the Free Religious Association, largely founded and run by Unitarians. It was a fascinating experiment with total freedom in religion, one that was not entirely successful.
Every association is composed of individuals, but it was the distinction of the Free Religious Association to be composed of individualists. Not surprisingly, this was not the recipe for a cohesive, enduring organization. In reading through the history of the Free Religious Association it can be maddeningly difficult to determine precisely what they believed in, which of course was in some ways the point. The Free Religious Association seems to have been less about the content of belief as about its absence, less an affirmation of any doctrine as the negation of any possibility of dogma. Just as freedom is essentially a negative connoting the lack of bondage, sympathy with the Free Religious Association consisted mainly of earnestly lacking the ability to remain comfortable within the fold of even the most liberal sectarian Christianity.
If a common core can be discerned in the Free Religious Association, it consisted of a commitment to individual conscience in religion, a universalism that expected that all religions reflect a certain measure of truth, a commitment to rationality (variously understood), and a general optimism about the future. If these sound similar to the commitments cherished by Unitarians of the time, that’s because they are the same. In an odd way, the Free Religious Association, and the Transcendentalists before them, represent a sort of Unitarian errand into the wilderness. Like the Puritans fleeing the Church of England the better to reform it, the Free Religious Association slipped away from the new National Conference of Unitarian Churches, and then proceeded to use essentially Unitarian thinking to argue for a rather post-Christian conception of religion. Much of their writing follows in the familiar vein of the Jeremiad, decrying the declension which they have finally fled, the better to hold to the spirit of true liberal religion. And like the Transcendentalists, they failed to sustain themselves as a movement, and ultimately had their largest impact on future generations of avowed Unitarians, who folded their ideas back into the denomination. This laid the ground for yet another Unitarian heresy that would appear in the next century: religious humanism.
Meanwhile liberal rumblings had been developing in American Judaism since the antebellum period, and it is not so surprising that Reform Judaism of the day, at least in the vein of Isaac Wise, looked rather like Jewish Unitarianism. The Jewish Reform movement was nothing if not an attempt to rationalize religion, making it modern, reasonable, and respectable. But the situation was complicated by Reform’s roots in Europe and its development in several different parts of the world. This is not a simple story of Americanization, even if the role of America can not be removed from the history of Reform. Therefore, it forces a re-evaluation of other Americanist narratives: how much of the change that we perceive in other religions in the United States is truly Americanization as Americanization, and how much is general adaptation to new situations that can be observed operating in parallel in other countries? Reform Judaism was far more successful than the Free Religious Association, and today is one of the largest and most vital Jewish denominations. One reason for this difference in fate would seem to be that while the Free Religious Association fled all tradition and lacked a cohesive core, Reform Judaism operated in the specific boundaries of a particular religious heritage, at times dramatically rethinking and paring the tradition, yet always in overt relationship to a shared body of ritual, text, story, and community.
Those who found even Reform Judaism too constrictive helped to fuel the creation of the Society of Ethical Culture. The emergence of Ethical Culture seems to be the basis for testing a general hypothesis: reformist movements in religion, especially those including an emphasis on individual conscience, will always generate their own dissatisfied reformers. Unitarianism reformed Protestant Christianity and in the process spawned the Free Religious Association; Reform Judaism reformed the Jewish religion and in the process beget Ethical Culture. The irony of such developments is that their adherents typically display a concern for corporate action and a desire to unify people, often through seeking a lowest common denominator in religion–yet the inability to retain people through a lowest common denominator approach to religion, both because it fails to meet all the needs of devotees and because no one can agree on what is common in the first place, means that such groups always contribute to the further splintering of the community and fail to develop large masses of adherents. The Free Religious Association and Society for Ethical Culture can rightfully claim that they have had an important and disproportionate impact on American religion and culture, but their small numbers prevented such movements from ever achieving their ambitious goals on a truly significant national scale.
Transient and Permanent 
Much of your bill of particulars against the 19th-century FRA would seem to apply to the 21st-century UUA as well. What might we do to avoid the FRA’s fate?
Is Baha’i a similar phenomenon within Shia Islam?