I would like to argue on both your definitions of what makes someone Jewish, and on your assertion that it is not inconsistent for an atheist to be Jewish.
When debating ideas regarding Judaism and theologically Jewish concepts, I do not think it is proper to use the definitions set by Hitler or anyone else who was or is so opposed to Judaism, but rather by the Torah’s definition of what makes someone Jewish because it is the guide for Judaism in the world. Leviticus 24,10 states that “ The son of an Israelitish woman, whose father was an Egyptian, went out among the children of Israel; and the son of the Israelitish woman and a man of Israel strove together in the camp. This shows that according to the Torah, the offspring of a Jewish woman and a non-Jewish man is considered part of the children of Israel in the same way that the offspring of a Jewish woman and a Jewish man is considered part of the children of Israel. Therefore, One is Jewish simply if his mother is Jewish, or he took the appropriate steps to convert into the religion.
The premise that “what makes someone Jewish is acceptance as Jewish by other Jews” is false. Is an isolated Jew unable to be Jewish if there are no other Jews there to confirm or accept him?! No, he is still Jewish. Even the adherence of Jewish practice does not qualify one as Jewish, and the lack thereof does not disqualify one from Judaism.
Although a person can convert to Judaism, it is a complex and precise process consisting of a Brit Mila for all men, immersion in the mikvah for both men and women, and a specific Bracha that must be said after the conversion ritual is complete. The mere act of beginning to follow Jewish costumes and practices, and even believing in Jewish values and ideas, does not actually make one Jewish for all intents or purposes, unless he has converted in the proper fashion. I would also like to note that although the “public affirmation of commitment” is becoming an increasingly popular tradition, it is not required in order to fully and completely convert to Judaism.
Although the Israeli government recognizes certain groups as “Jewish”, this does not necessarily qualify them as being Jewish in accordance with The Torah. Regarding the Law of Return amendment, 1970, The Israeli government recognizes the child of a Jew (even if only the father is Jewish), the grandchild of a Jew, the spouse of a Jew, or the spouse of a child of a Jew, or the spouse of the grandson of a Jew. The political definition and recognition of a Jew does not necessarily mean that he is actually Jewish according to the definition and law of the Torah.
I do not want to argue with what is important and not important in Christianity because that is simply an area in which my knowledge is quite limited. However, your perception of what is important to Judaism is fundamentally incorrect. Belief and action are both supremely important in the Jewish religion. Your statement that “Abraham was not told to BELIEVE in God, but rather to walk with God” is absurd. How can someone fulfill a direct request of someone that he does not believe to exist? However, I can’t argue with you that in Judaism “doing the right things for the wrong reasons still means you’ve done the right thing.” I don’t think that it is the best way to do the right things but it is still considered as if you did them. In Gemara (Talmud) Nida 61a, God tells Moses not to fear battle with enemy giant of Israel, Og, king of Bashan. The Gemara asks “Why was Moses afraid of Og?” The answer is that, when Lot, Abraham’s nephew, was captured in battle, Og ran to Abraham in order to tell him the news so that Abraham could go and save his nephew’s life. The Gemara explains that although Og ran to Abraham and told him about Lot only so that Abraham would die in the war and then Og could take Abraham’s wife, his actions actually resulted in the saving of Lot’s life and were therefore good. Moses was afraid that because of the great merit of saving Lot’s life, Moses would not be able to defeat Og in Battle. This gives great credit to the statement that in Judaism “doing the right things for the wrong reasons still means you’ve done the right thing.” However, the Gemara continues and states that God said to Moses “don’t be afraid” and Moses jumped up and struck Og in the ankle, and Og fell and died. This shows that good actions without good intentions to back them up are not as good as good actions with good intentions.
Furthermore, Judaism is not only about actions, but it is about believing in God as well. The first of the Ten Commandments, the foundations of Judaism, is “I am your God…. Thou shalt have no other gods, aside from me.” Other foundations of Judaism include “know before who you stand” (referring to God) and “Love God with all your heart and all your soul.” The Shema, The most famous Jewish Phrase, “Listen O Israel, God is our master, God is One.” The belief in the existence of God is so intertwined with the practice of Judaism that it is impossible for Judaism to be practiced without a belief in God.
I would like to conclude by noting that If one is born Jewish and decides that God does not exist, the Jewish religion does not offer a way to convert out so technically he would have to remain Jewish while being an atheist, thereby making him a Jewish atheist. However, it is impossible for an atheist to truly practice Judaism.