Note that for over 150 years, very low status people had come to America, worked hard, and became middle class or better people within a generation.
That wasn’t all that common in the Old Country. Ben Franklin, for example, was appalled when he visited the UK to find class snobbishness permeating every level of society. In the UK, who your parents were, etc., mattered tremendously. In the US is didn’t.
The class consciousness (which still permeates the UK), affected everything. Incompetent boobs became judges, military officers, and even King solely based on their parentage.
At the other end, if you were a hard working son of peasants, your chances of moving up in life were small. It was actively discouraged. This just ran counter to the American experience.
So anti-royalty was just part of a sentiment that “We don’t care what your great grandfather did for a living, what are you doing to make a better life?”
(Slaves, excepted, of course.)