There will be always someone offended and the means used are the essence of the message so I don't think there is too much room for adjustment. For me the important part is the newspaper itself and I simply don't expect NYT to come up with a primitive, stereotypical and racist cartoon.
The Indian newspaper, they made IMHO idiot out of themselves but I can understand the reaction. It is pretty typical for somebody who was and is a subject of different stereotypes too often.