In order to be a moral agent one needs to have a commitment to speak the truth and to certain basic moral norms or patterns of action. This commitment, in crucial situations, needs to be practically as strong or direct as perception.
I do not choose to see the things which I in fact see; my perceptions may be partially illusionary (or delusional), but it's all I got. (That is, all I got at any moment of time. We can train ourselves to be better, more careful observers. Perception is not an all-or-nothing phenomenon.) Similarly with feelings and dispositions: I may be afraid to act, but somehow find it in myself to still do so. Or I may be tempted to to act, but somehow still find it in myself to refrain from acting. When I feel guilty or proud about something, I did not choose (at that moment in time) to feel that way; it's just a psychological given which will propel me forward; I will only occasionally, in a limited way be able to "take a step back" and reflect on those feelings and perhaps tweak them - again analogous to perception.
I believe we're all aware of this and we all recognize the necessity of commitment (which I consider a better word than "intent" or "intention") in performing morally praise-worthy and blame-worthy actions. Moral realism has some sense, but only in sofar as it expresses (in an akward and misguided way), the "givenness" of this commitment; only in sofar as our specific reflexive moral feelings, intentions, dispositions (like guilt or courage) are (at any moment in time) "given" to an individual.
Without assuming moral realism we can establish "objective" norms by (1) expressing those norms as clearly as possible (or putting forward certain examples, telling stories and parables) and (2) achieving intersubjective agreement about them (agreement about what those norms are - that is, how to recognize actions falling under them - and agreement about how to relate different norms and values to each other).
If we do so, we might or might not also assume moral realism as theory. But (assuming moral realism is coherent) what would be gained by that? Would it make one's commitment stronger? Would it somehow ensure that all norms we established are unchangeable? Would it really change why we are committed to this or that norm or value?
If the source or evaluative basis of our ethical norms is a transcendent divine source, how does that help in making the norm more "objective"? Do we (have to) follow the norm because a sacred text posits it as God's command and because otherwise God will punish us, or does God command this or that norm because acting in that way is good? Is God an autocratic God and ethics basically a form of blind obedience? Or does the particular selection of values -- for instance, the values expressed in the Sermon on the Mount, the value of care for the vulnerable, the value of social justice, or the value of universal brother- and sisterhood -- does that reveal something about what or how God is?
If it's the last, then, in the eyes of a religious person it might be strange that an unbeliever doesn't see ("as through a glass darkly") God in those values or in living according those values, but this also seems to imply that we all can (in principle) make those same evaluations without having to refer to a divine source (or without being aware that there is a divine source behind it).
Now, speaking of sexual morality. According to Matthew 19:12
there are eunuchs who have made themselves eunuch for the sake of the kingdom of heaven
One of the early, very important church fathers, Origenes of Alexandria, took this quite seriously - and literally - and either castrated himself or had someone else perform this operation on him. (Medieval monks were also not as prudish as modern Christians, so Wikipedia includes some colorful illustrations of the act.) Most Christian men have not followed him in this. Who was "right"? How did the fact that all those men saw and see the Gospels as God's Word help them decide which values and norms actually to follow?