The Royal Society didn't take over government functions, they just provided advice to the government. And in any case not all puritans came from the UK, federal laws in the US were very nearly printed in German as well as English.
In 1660 when England reinstated Christmas during the Restoration (the Royals knew that bread and circuses was important), Boston didn't celebrate it until the mid 19th Century because of the Puritans didn't hold with any of that debauchery. The American Restoration Movement also had several Christian factions which didn't celebrate Christmas, and that's well after the founding fathers declared independence (and the founding fathers didn't really do a good job of the constitution either, it's been bulldozed in less than a year).
Oh, and that lack of holidays and workers rights? The Puritans again.
Please enjoy your modern-day Christian Nationalism. On second thoughts enjoyment probably won't be allowed either.