I don’t think deontology requires a belief in God at all, though it is reduced to some set of self-evident (from the holder’s perspective) truths. For example, I believe the right to be left alone is axiomatically a right.
But I think we all are both, and we tend toward one end of the spectrum or other. As another example, I believe balancing natural (God-given if one prefers) rights with their impact on others’ rights and duties is perfectly appropriate. That goes for free speech, the right to bear arms, etc. No right is absolute, and their restriction is largely (and properly) based on the exercise’s effect on other people.
So, yes, they are in conflict. But except for the fringe on either side, I think most of us are “balancers.” We just disagree on where to draw the line.