Are we allowed to criticize a black president?

Consider the rhetoric that has been incessantly hurled with no holds barred against our current President. Assuming that a "joking" morning show host could hurl visceral epithets or "funny" innuendo at the President of the United States, would the "funny" "jokes" be allowed in the context of a black president?

Currently, the media is reportedly enamored with a can-do-no-wrong eligible alternative to the presumptive Republican candidate. If the run-up to the primaries, and then the general election, allow a relatively inexperienced candidate to pass mostly unquestioned and potentially unscathed, is that because of the "idea" of the "ideal" or is it because to look at the naked emperor and call him on it is so horrible?

Perhaps, there is nothing to be called out upon. More power to such people who yet exist in this world. However, there is the premise that any questioning of a non-white must inherently be racist. Serious? Welcome to France. I think the big question is who is crying racism, and whether racism is being called out to obscure the question. "You can't say that! He's black, and he's President of the United States! Don't disrespect the man or the office!" What is interesting is that these statements will absolutely and unequivocally be shouted from the rooftops by well-meaning people who may have had no qualms saying infinitely more scandalous remarks against a sitting white President.

Can a purely objective criticism ever be levied without the taint of racism being implied? It should really depend on the people who feel that racism is evident in every bit of speech (and those who are influenced by those people). But those are the people whom we probably can never criticize.