To avoid such unpleasantness in the future, perhaps the New York Times editorial board should publish a cross-tabulated list broken down into three categories:
A. Which demographic groups are A-Okay for anybody to parody
B. Which demographic groups can never be parodied by anybody, and
C. By far the longest section: which groups can be parodied by some people but not by others. This can be very finely calibrated. For example, Assemblyman Hikind is a Democrat and Jewish (good), but an Orthodox Jew opposed to gay marriage (bad).
In contrast, Saturday Night Live put Fred Armisen in blackface for years to do President Obama, with virtually no protests. Was this because Armisen is a little bit Japanese? Or was it because SNL could never think of anything funny to say about Obama?