Is the word Jap and Japs racist?

No, they aren't since Japanese isn't a race. It is a nationality and I am always surprised by the numbers of people who don't know the difference between race, ethnicity or nationality.

Part of me feels it is a derogatory word but another part of me just thinks its short hand for Japanese. Its seems like it would be the equivalent of someone calling me a Cali because im from California. Is the currency Euro considered derogatory and is Tex-Mex double racist?

I have never heard "Jap" used by someone that respects Japanese people. I would not say "Jap"; I would say Japanese.

A few years ago I was talking with someone and I said "Jew" but I think I hesitated a bit; I was not sure how to refer to a Jewish person (individual). The person I was talking with said he is Jewish and that it sounds like I don't like Jewish people. I said no, that I like Jewish people (I was renting a room with a Jewish couple). I guess that "Jew" is also improper but I am still not sure how to refer to a Jewish individual. I should hang out down the street at the Jewish Technical School. Or talk with a friend of mine that is Jewish.

I don't understand why "Redskin" is derogatory. Since the Washington Redskins call themselves Redskins it is obvious they don't intend to use the word in a negative way.

Logically, it seems totally appropriate to say "Jap" but I think it is best to avoid it if you respect the Japanese people. As far as I know, they don't want you to and that is very important.