Sorry, dude. That doesn't work for us. We, the People of Israel, accept as Jews those with a Jewish mother or who have gone through a formal conversion to Judaism. There are plenty of people who accept the God of Abraham who are not Israel, aka are not Jews.
You are correct that it is not "genetic," but it is more complex than you are making out. Let me give you two examples:
1. Let's say a person has a Jewish father, but not a Jewish mother. Even though he gets "Jewish DNA" from his father, he is not a Jew at all. In order to be a Jew, his mother would have to be a Jew (even if the father is not).
2. Converts do not have any "Jewish DNA" at all, and yet are 100% Jew. This is because we are a tribal people, and as with other tribes, a person can be adopted in. In this case, that means a formal conversion to Judaism. They would of course marry a fellow Jew, and their children would not only be Jews via the Jewishness of the mother, but the children would also have the shared ancestry.
I realize this is difficult for modern people to understand. In modernity, most people have boxes for "race," "nation," and "religion." The box for "tribal people" just no longer exists in most people's minds, and so they are at a loss for which box to put us into.