A significant portion of the population in Israel is secular. Indeed, on Rosh Hashana, the Jewish New Year, the beaches in Tel Aviv are crowded with Jews enjoying the sun and surf. By your definition, none of these people are Jewish because failing to attend religious services on one of the High Holy Days must mean they do not believe in God. The same applies in our country. Many Jews, liberals and conservatives alike, are not religious, but identify with their Jewish heritage and culture. This does not make them any less Jewish than the once or twice a year Jews who attend synagogue and then ignore the religion the rest of the time. All are Jews and, just like everyone else, their views are not all the same on things like religion, politics and economics. But, it doesn’t make them less Jewish, less patriotic or less American. And, it certainly doesn’t turn all non-practicing Jews into socialists.
Not my definition, none of these people are Jewish...
Romans 2:28-29
God doesn't break the Covenant with man. Man breaks it.
In the U.S., Leftism is the default ideology for non-religious Jews.