When Jews speak about our laws having a "moral basis", what do they mean? I can never tell.
My guess is that are making the same distinction that Catholics make between "ritual" laws and "natural" law.
According to the Church, Jesus canceled the ritual law, but not the moral law which is any law that can be known by reason. Cain, for example, could be punished for killing his brother, though the Torah hadn't yet been given, because murder is wrong under natural law, and Cain was responsible for knowing this through reason. According to Catholics homosexuality is also wrong under natural law, and would be wrong even if the Torah had never outlawed it.
But there are a few problems with this approach. First, Jews do not recognize any distinction between ritual and natural law. We do recognize a distinction between chok and mishpat but no two rishonim agree on what constitutes the distinction. To the best of my knowledge every proposed system has counterexamples. For example, some propose that a chok is a super-rational law, or a law with no reason, but the best example of a chok, the Chukat Hatorah or Parah Aduma, has been explained by Rambam and Rashi (following Moshe Hadarshan)
More importantly, natural law is based on the idea that the rules of life can be worked out through reason, but this idea has been discredited multiple times over. Reason, unfortunately is notoriously flexible. It can be employed to justify or discredit just about anything. This is why I say that subjective, human-made morality is the only kind of morality there is. Even if we stipulate that God revealed commandments, all subsequent "morality" is based on how we human beings choose to understand, interpret and apply those commandments and/or whatever other sources of morality we have chosen to accept.
"Moral Law" is just whatever human beings happened to develop through whatever process they happened to use.
Search for more information about morality at4torah.com
Search for more information about morality at4torah.com