Is it weird to be American and be a royalist who dislikes the American form of democracy?

You are an American royalist who thinks the USA's version of democracy isn't brilliant. That is no more weird than someone in the UK being anti-monarchy, and having a problem with the voting system. Some might question your view of history, but your issues with certain forms of democracy and even support (or at least not the violent dislike propagated by many) of a monarchy within a democracy are probably views that more people share than would like to admit it. Just because you were born in the USA doesn't mean you have to agree with how the country works, or agree with the average American's view on things. The world would be pretty boring if everyone agreed all the time, after all.