I think Iron Patch and Kray Gelder may be right... It seems these buttons were commonly thought to be related to Washington Inauguration, but they were in fact Scottish Rite Masonic buttons. The obvious link being that Washington is a Master Mason of the Scottish Rite. Awesome find though none-the-less!
It's all about joining forces and learning here right? So let's explore this just a bit...
Why could this button be confused with a George Washington Inaugural Button?
Well, here is what I think...
We know that Freemasonry played a huge part in the Colonization of America and the forming of it's government. The 13 rattles on the snake could very well mean the 13 original Colonies. The rattlesnake symbol is synonymous with American Colonialism.
Examples...
The Gadsden "Don't Tread On Me" Flag...
It was designed in 1775 during the American Revolution...
From Wikipedia:
Snake symbolism in Colonial America
The timber rattlesnake can be found in the area of the original Thirteen Colonies. Its use as a symbol of the American colonies can be traced back to the publications of Benjamin Franklin. In 1751, he made the first reference to the rattlesnake in a satirical commentary published in his Pennsylvania Gazette. It had been the policy of Great Britain to send convicted criminals to the Americas, so Franklin suggested that they thank the British by sending rattlesnakes to England.[2]
In 1754, during the French and Indian War, Franklin published his famous woodcut of a snake cut into eight sections. It represented the colonies, with New England joined together as the head and South Carolina as the tail, following their order along the coast. Under the snake was the message "Join, or Die". This was the first political cartoon published in an American newspaper.
As the American colonies came to identify more with their own communities and the concept of liberty, rather than as vassals of the British empire, icons that were unique to the Americas became increasingly popular. The rattlesnake, like the bald eagle and American Indian, came to symbolize American ideals and society.
As the American Revolution grew, the snake began to see more use as a symbol of the colonies. In 1774, Paul Revere added Franklin's iconic cartoon to the nameplate of his paper, the Massachusetts Spy, depicted there as fighting a British dragon.[5] In December 1775, Benjamin Franklin published an essay in the Pennsylvania Journal under the pseudonym American Guesser in which he suggested that the rattlesnake was a good symbol for the American spirit:
Another example:
Just something to think about in regards to a possible correlation.
