It's the monochrome nature of the internet
heres a good quote on washington and adams
The country's first two presidents, George Washington and John Adams, were firm believers in the importance of religion for republican government.
As citizens of Virginia and Massachusetts, both were sympathetic to general religious taxes being paid by the citizens of their respective states to the churches of their choice. However both statesmen would have discouraged such a measure at the national level because of its divisiveness.
They confined themselves to promoting religion rhetorically, offering frequent testimonials to its importance in building the moral character of American citizens, that, they believed, undergirded public order and successful popular government.
from:
Religion and the Federal Government, Part 1 - Religion and the Founding of the American Republic | Exhibitions (Library of Congress)
you are right religion was thought to be importiant for morality but it was general religion not just christianity, considering neather of them was a christian but a diest (if you want to bring up thier beliefs i got quotes from people who knew them, including reverends)
washington in his farewell speech did consider religion nessicary for happiness as well
The Farewell Address
In his Farewell Address, the first president advised his fellow citizens that "Religion and morality" were the "great Pillars of human happiness, these firmest props of the duties of Men and citizens." "National morality," he added, could not exist "in exclusion of religious principle." "Virtue or morality," he concluded, as the products of religion, were "a necessary spring of popular government."
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