The question is vague and mixes up too many undefined things. What is religiosity versus non-religiosity? Are you equating “being religious” to holding to specific religious doctrines, as preached by the churches and sects? Do you suppose that everybody defines morality in the same way?

But I guess what you are trying to get at is, how will one behave if one’s religious beliefs do not include an all-powerful spiritual overseer that threatens to harshly punish all of our evil acts, thoughts, words, deeds. And that has nothing to do with morality, only with a fear of punishment. If your feelings and inclinations are to do evil, then not doing so because of fear is not morality but hypocrisy. How many of the church-going “religious” people are only hypocrites? Millions. How many of the “non-religious” have a solid and true morality? That is more difficult to ascertain.