Yes, definitely. Japanese American civil rights and human rights organizations have campaigned to stop Americans (and any other English-speaking peoples) from using this word because of its racist, insulting, and disrespectful connotation. Americans used "Jap" carelessly, casually, and indiscriminately before, during, and after World War II, with all the negative contexts you could think of (dirty Jap, damn Jap, goddamn Jap, kill the Jap, slap the Jap, etc.), so there has been a drive to stop the usage of this word and to raise Americans' consciousness on the harmful effects of the word "Jap."
The dictionaries are the final arbiter on the usage of words, and here is what they have to say on "Jap."
American Heritage Dictionary: Jap. Offensive Slang. Used as a disparaging term for a person of Japanese birth or descent.
American College Dictionary: Jap. Colloquial and derogatory. Japanese.
Random House Webster's New World Dictionary: Jap. Slang (disparaging and offensive. Japanese
Webster's New World Dictionary: Jap. Short for Japanese: a hostile term.
So there you have it. The word is offensive, derogatory, disparaging, and hostile, according to the dictionaries, so people of goodwill and intelligence know better than to use it.
Random House Webster's New World Dictionary: Jap. Slang (disparaging and offensive). Japanese.
Webster's New World Dictionary: Jap. short for Japanese: a hostile term.
So there you have it. "Jap" is a disparaging, derogatory, offensive, and hostile word, according to the dictionaries; and people of goodwill and intelligence will refrain from using it.