believing as they do.

Does "believing as they do" refer to "believing just like they (liberals and moderates) always would like to believe"?

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In talking about the good consequences that your beliefs have on human morality, you are following the example of religious liberals and religious moderates. Rather than say that they believe in God because certain biblical prophecies have come true, or because the miracles recounted in the Gospels are convincing, liberals and moderates tend to talk in terms of the good consequences of believing as they do. Such believers often say that they believe in God because this "gives their lives meaning." When a tsunami killed a few hundred thousand people on the day after Christmas, 2004, many conservative Christians viewed the cataclysm as evidence of God's wrath. God was apparently sending another coded message about the evils of abortion, idolatry, and homosexuality. While I consider this interpretation of events to be utterly repellent, it at least has the virtue of being reasonable, given a certain set of assumptions.