The social pain of disapproval serves the same purpose. When social disapproval is inline with God's Word, that pain has a greater possibility of leading people to examine their contrary beliefs/behavior and turn back to the right path - repent.
Giving the legal permission to do what is wrong salves over the conscience and allows the lost a greater comfort in their wrong doing.
Whether it is legalization of abortion, sexual deviancy, or any other of a myriad of things the Bible is abundantly clear is wrong, legalization has the effect of sending more people to hell. Or, at the very least, prolonging their self-deception until they finally come to the end of themselves and reach out for God but still suffer the natural consequences of the much deeper hole they are in because of the comfort of legalization.
This is not a trivial matter - it is grave, immediate, and important. We should be saying to those we've elected, "How dare you vote contrary to God's Word!"