This is an old trope of many religious people. To them, their religion or their deity is the source of morality, in which case those who reject gods and religion must be immoral.
New research shows that morality developed in humans independently of religion.
Considerable debate has surrounded the question of the origins and evolution of religion. One proposal views religion as an adaptation for cooperation, whereas an alternative proposal views religion as a by-product of evolved, non-religious, cognitive functions. We critically evaluate each approach, explore the link between religion and morality in particular, and argue that recent empirical work in moral psychology provides stronger support for the by-product approach. Specifically, despite differences in religious background, individuals show no difference in the pattern of their moral judgments for unfamiliar moral scenarios. These findings suggest that religion evolved from pre-existing cognitive functions, but that it may then have been subject to selection, creating an adaptively designed system for solving the problem of cooperation. (Emphasis added.)
Note that this sense of morality is found in children who have not yet had the possibility of religious indoctrination. There was a good episode of WNYC’s Radio Lab, Morality, dealing with this also.