We are ALL Jews,if we are born to a Jewish mother.If we're in the USA we're American Jews,in Spain,Spanish Jews. A Jewish American would mean you are always an American,yet happen to be also Jewish or anything else.If I settle in England,I remain a Jew;an English one,not an American Englishman.I AM JEWISH
I think it depends on the social context, as in, who you're talking to and why you need to call yourself anything like that to begin with. I mean, if you're among yidden, they know you're a yid - and that you're most likely american, so I don't see where that would even come up. If for whatever reason a goy or a frei yid asks, then I would respond that we ourselves are a nation of am yisroel, yet we have to be very grateful to the medina that hosts us and makes life a lot easier for us to be able to learn torah and be jewish.
Which is the adjective and which is the noun? The noun is always the name and the adjective is descriptive. If one says American Jew he would mean that the noun Jew is what is important and the adjective American is simply descriptive. If one says Jewish American then American would be the noun and of primary importance. It's reminiscent of those who called themselves Germans of the Mosaic persuasion.
I think if I were asked about my right to vote in an American election, that context would dictate that I reply that I am an American, and would never try to hide the fact that I am a Jewish American.
And if I were being asked about my Minhagim, such as if I were visiting Israel (alavi!) for Shavuos, and how many days of Yom Tov, I'd say that I am an American Jew required to observe 2 days of Yom Tov even if I am visiting Israel at the time.
This reminds me of a story about two American soldiers in Saudi Arabia during the Gulf War who had been issued new dogtags with religion designation "protestant B" or something and each had made the same private personal decision to ignore this opportunity where the US military thought they might want to hide their religion so allow them to step on arab soil by arab law.
Jewish is what binds all of us Yidden togther,nomatter where we are. So I am always a "XXXXX" Jew.Jew is always the noun.I am a man.If I live in the USA I am an American man.If I'm in France I'd be a Frenchman.I am a Jew. In America I'm an American Jew,In France I'd be a French Jew. If I keep mitzvos,I am a "frum " Jew,if I don't;I'm a secular Jew.
The Shevet goes by the father,Jewishness goes by the mother. It is a given who the baby's mother is,so the baby is Yisroel and gets a bris,if the mother is Yisroelis. The baby is a Cohen or Levi or Yisroel,depending on the status of the father.yerusho goes according to the shevet,as per the father's shevet. If the mother was a non-Jew,the child is NOT a Jew. See parshas Pinchas,the Shevotim are numbered there.The families are after the fathers.
This is really scary - that is 100% kefira my friend, do you think you know more than chazal? It's called mesora..meaning, we don't know how to interpret pesukim. We're not christians who go around quoting the torah's verses to prove points without understanding them - chazal, the rishonim, and everyone, all say that jewish-ness is passed down through the mother.
It's not the majority. It's everyone, as in, all of klal yisroel, because we have mesorah. It's not "rabbinic" - you sound like a christian to be honest.