From what I've heard when I was growing up in New York is that after the English came to New York and displaced the Dutch, there was a kind of anti-Dutch bigotry, evidence of which lingers in expressions like "Dutch treat" (which is really no treat at all, since you're paying for your own meal) and "Dutch courage" (which is really not bravery at all, but rather the loss of inhibition you get from drinking).
I have no idea, though, about what that says about the jump rope game Double Dutch.