Religious fundamentalists (including Jews) claim moral superiority because their morality is absolute, from God, as opposed to secular and humanistic values, that shift over time. Herein lies the biggest flaw in their ideology.
Any serious student of Jewish history and halachah knows that Jewish law and morality has shifted over time. This is true for all religions. Even for the ultra-orthodox morality and law is not absolutist but evolved over time (albeit more slowly than general society), given societal pressures. Their morality is a function of the society with which they identify. Yes, it is anchored in an ancient tradition through a process, but it definitely shifts.
Think about attitudes about women, relations with non-Jews, slavery, economics, sacrifice, etc. To assert that Jewish ethics is absolute is completely ridiculous. A good book about this topic is "T'murot B'sadeh Hahalach", by Akiva Sternberg (in Hebrew).
As far as God being the source of morality, I would posit that most religious people observe their ethical norms because of the societal structure that they live in, not because of God, since clearly they have to determine what God wants of them through man's interpretation ("an eye for an eye", etc). Do not kill? It depends who is doing the killing and the being killed!!Would a Beit Din now burn a prostitute? This "intepretation" changes due to societal pressures and circumstances.
Just like American culture is a function of American history, laws, norms and societal pressure, Judaism started as the ethical and legal system of ancient Israel, and bears little resemblance to modern Judaism (even though many ultraorthodox like to believe that they are observing Judaism like they did during the Temple era).
IMHO, morality is a man-made construct to make society more livable, and is part of our emotional makeup. Religion then adds holiness to it and gives it metaphysical meaning. This perhaps strengthens it but also makes it resist the inevitable adaptation and change. Maybe for the better but who knows?