That group is still around. You may view their official site here.
As this relates to Washington and religion, in "George Washington's Sacred Fire," Peter Lillback cites Washington's thoughts on Lathrop's sermon as evidence of his orthodox Christianity. Indeed, Lillback repeatedly notes Washington's special praise for the address, that he received it with "singular satisfaction." Lillback also claims said Humane Society was "deeply committed to historic Christianity." (p. 671.) Lillback's book defines "historic Christianity" as "orthodox."
The problem is, it's likely that Rev. Lathrop was not an orthodox Christian AND a number of the founders of the Humane Society were committed Unitarians.
From the official site:
Formally established in 1786, The Humane Society of the Commonwealth of Massachusetts elected James Bowdoin, the governor of Massachusetts and the founder of Bowdoin College, to be its first president. The other original trustees were Rev. John Clarke, Dr. Aaron Dexter, Rev. Dr. Simeon Howard, Rev. Dr. John Lathrop, Rev. Samuel Parker, Dr. Isaac Rand, Dr. John Warren, Dr. Thomas Welsh, Dr. Benjamin Waterhouse and Judge Oliver Wendell. In 1791, The Humane Society was formally incorporated in the Commonwealth of Massachusetts.
One of those unitarians, Dr. Waterhouse, corresponded with Thomas Jefferson. Jefferson felt comfortable writing what follows to Dr. Waterhouse:
... The doctrines of Jesus are simple, and tend all to the happiness of man.
1. That there is one only God, and he all perfect.
2. That there is a future state of rewards and punishments.
3. That to love God with all thy heart and thy neighbor as thyself, is the sum of religion.
These are the great points on which he endeavored to reform the religion of the Jews. But compare with these the demoralizing dogmas of Calvin.
1. That there are three Gods.
2. That good works, or the love of our neighbor, are nothing.
3 That faith is every thing, and the more incomprehensible the proposition, the more merit in its faith.
4. That reason in religion is of unlawful use.
5. That God, from the beginning, elected certain individuals to be saved, and certain others to be damned; and that no crimes of the former can damn them; no virtues of the latter save.
Now, which of these is the true and charitable Christian? He who believes and acts on the simple doctrines of Jesus? Or the impious dogmatists, as Athanasius and Calvin? ...
Regardless of whether the members of the Humane Society or, for that matter, Washington himself, were as extreme unitarians as was Jefferson, they all shared a very man centered theistic creed.