We don't get to "agree to disagree" about objective reality. Yes, man is a wholly subjective being. And yes, each has their own experiential reality. But that perceptual experience depicts a world of certain constants. We cannot know that the tree we perceive exists outside our experience (in fact, we cannot know that anything exists outside our experience), but this is irrelevant as long as that experience produces consistent phenomenal cause-and-effect relationships - and it does.
Walking into a brick wall consistently yields a bump on the forehead. Never do you simply pass through it. Certain behaviors have certain predictable results. As long as this continues, we can assert de facto objectivity, even if our subjective nature obviates certain knowledge of true, independently-extant objective phenomena.
In this way, the term "objective" can be redefined to include the caveat of man's subjective nature without any alteration to the practical meaning of the word. Personal experience and subjective consensus between beings about the sun being in the sky will serve all the purposes of its true objective existence, whether it actually exists outside our conscious perception or not.
So, yes, for all intents and purposes there is such a thing as "objective" reality, and this includes natural law cause-and-effect. In fact, if you think about it, morality is rather tautological, and thus self-evident and irrefutable...
Bad (immoral) actions are bad because they're bad. What makes an immoral action negative is its negative consequence, but that consequence is an inherent part of the action within a particular set of circumstances. All we're really saying here is that actions with bad consequences have bad consequences. Morality is just a description of reality; it adds no new content. It's not another level of qualification, and it requires no external source, be it divine or cultural. The moral nature of an action is a factual description of the action itself.
Immoral action is defined by its context, which includes its consequences. If I take a cookie from you, this action may be moral or immoral depending on whether you gave your consent to my taking it. The action of cookie-taking is neutral, but when performed within a certain set of circumstances, the consequences can be quite different. The only thing that makes one such cookie-taking immoral (theft) and the other moral (graciously receiving a gift) is the negative consequence.
The negative consequence of all immoral action is the creation of an environment that inhibits the authentic expression of the being in question. In other words, immoral actions do not permit full expression of man's free-will autonomy, which is inherent to his nature. This is what defines the action as immoral. The action does not duly acknowledge the reality of the being. It is a denial of truth. It is a lie.
So immorality is simply acting out of accord with truth - of course this will have negative practical consequences (just like ignoring the heat of a hot stove, or the immutable effects of gravity). More importantly, the immoral action is itself a negative, being an action inspired by error. We do not need to understand some complex chain of causality to see this. There is no leap to make. We need not understand anything more complex than "A is A" to see that morality (acting in accord with truth) is an absolute imperative under any and all circumstances, and that immoral action can never be prudent, desirable, or necessary.
RE: Human Rights Are Not Subjective