Organized religions certainly have their own standards for morality, yet morality is not something that is confined to religious individuals. In reality, however, it would seem to be somewhat more complicated than that.
Morality seems to exist on several different levels.
Individuals have their own personal morality. As you combine people into larger and larger groups or change the yardsticks by which you group them, you find a different set of moralities for each different group. Disputes are normally resolved at the lowest group level according to that group's moralities. If no agreement can be reached, the question is decided at the next highest level and so on. Problems arise when the highest levels of government and the judiciary attempt to pass blanket legislation that will apply to everybody.