I don't think we are upholding many morals that aren't already deeply connected to property rights and the laws that protect them. Most of the "victimless crime" sort of moral codes - abstaining from sodomy, honoring your parents, showing courage, avoiding graven images - are really no longer considered at all outside of specific enclaves.
Those moral codes weren't just social attitudes when they were written, remember, they were being set down as laws. Religion and belief weren't private things, they were the formal system of government for a specific group of people, with clear rules for who was in charge, inheritance and property, taxes, penalties and fines, in addition to the laws governing social behaviour.
Looking specifically at the Abrahamic faiths (which, taken together, is where the majority of humans draw their moral ideals) this is evident in the Torah (the first five books of the Old Testament) of Judaism and the Quran of Islam, but not so much for early Christianity. Early Jews and Muslims were setting down the rules for self-governance, while the early Christians weren't a "people" in the same way; they were subject to Roman rule and the laws of the states where they lived, and without the authority to administer legal decisions and punishment on their own behalf, which is reflected in their scripture. (There's this really good non-religious book,
Rome and Jerusalem: The Clash of Ancient Civilizations by Martin Goodman, that delves into the relationship between the Jewish and Roman cultures and states and the early Christians.)
Can you think of any morals that are strictly adhered to by the general population that aren't also the subject of law? I wasn't able to.
If we feel strongly enough about something that the general population strictly adheres to it, we tend to enshrine it in law so that we can legitimately enforce it and punish those who deviate. And it goes the other direction too. As something seems silly or irrelevant or unjust to the general population, we eventually drop it from our laws. (It may linger in the written code for long time, but enforcement stops.)
How social & moral attitudes influence law creation is a super interesting subject, like the history of the Temperance movement, prohibition, and its repeal, in 20th century America is fascinating.