I don't think there is a stereotype of foreigners as being lower class. There is a sort of repressed persecution complex, but "dismissive stereotypes about foreigners as something like animals"? No (at least if you're white)

DaShan's popularity is enduring - you get over the novelty of his skin color pretty quickly. After that you find he is genuinely funny and skilled at his craft. "Dancing Monkey" suggests that the audience is laughing at him rather than with him, which I do not think is the case.