It’s not the absence of belief in God, but the absence of God that undermines objective morality.
Do moral dilemmas provide good reasons to deny moral absolutes?
Is it possible that you know some actions are morally right or wrong even though you can't demonstrate it?
Since different cultures have different moral values, then morality must be relative to each culture, right? And to be truly tolerant we must hold that all moral views are OK, right? Not so fast. How much thought have you really given to these beliefs?
Can human flourishing ground objective moral obligations?