These examples illustrate why the underlying standard of morality is necessarily independent of religious claims — otherwise, there is no way to distinguish between various mutually exclusive religious claims on moral subjects and discern which of them are, in fact, based on valid morality.
You've got a good point there. You're in agreement with the Apostle Paul when says,
"Indeed, when Gentiles, who do not have the law, do by nature things required by the law, they are a law for themselves, even though they do not have the law.
"They show that the requirements of the law are written on their hearts, their consciences also bearing witness, and their thoughts now accusing, now even defending them." (Romans 2:14-15)
The Catholic West has a tremendous, millennium-long heritage of reflection on Natural Law --- a philosophy which gave birth to International Law via such thinkers as Bartolome de las Casas and Francisco de Vitoria, and crucially influenced even our own Declaration of Independence ("the separate and equal station to which the Laws of Nature and of Nature's God entitle them,") and Constitution.