Is it true that there is no absolute morality?

[SteveII]

I think that you're only describing how you would feel, if you stopped believing, Steve...not any logical conclusion of atheism.

Perhaps, but there are atheist philosophers who reason the same way Sarte, Camus, Nietzshche, Russel. You might be fine  with no ultimate significance, meaning value, or purpose. Others find that depressing.

Like Bertand Russel 

Such, in outline, but even more purposeless, more void of meaning, is the world which Science presents for our belief. Amid such a world, if anywhere, our ideals henceforward must find a home. That Man is the product of causes which had no prevision of the end they were achieving; that his origin, his growth, his hopes and fears, his loves and his beliefs, are but the outcome of accidental collocations of atoms; that no fire, no heroism, no intensity of thought and feeling, can preserve an individual life beyond the grave; that all the labours of the ages, all the devotion, all the inspiration, all the noonday brightness of human genius, are destined to extinction in the vast death of the solar system, and that the whole temple of Man’s achievement must inevitably be buried beneath the debris of a universe in ruins--all these things, if not quite beyond dispute, are yet so nearly certain, that no philosophy which rejects them can hope to stand. Only within the scaffolding of these truths, only on the firm foundation of unyielding despair, can the soul’s habitation henceforth be safely built. https://users.drew.edu/jlenz/br-free-mans-worship.html

I am not trying to say that you are not happy with your belief--if you are, great. But it is obvious others struggle.

---

 So I am willing to grant assumptions both atheistic and theistic approaches could share such as, the existence of conscience and the cultural contingency of all moral systems, etc. with the understanding that these are ultimately grounded in moral absolutes that transcend any individual or culture.

I think that you'll find immense overlap in religious(particularly divine or "godly") and secular moralities.  That's mostly due to there being nothing in any religious morality that could not be used in a secular morality other than "because god said so/made it so".  Anything in a religious morality that does not depend strictly and solely on god saying so/making it so will find it easy to fit into a secular morality.  Similarly, many religious moralities have leveraged secular moral proclamations.  Reciprocity is, ofc, the famous example familiar to most christians.

You and I, in all likelihood, think that many of the same things are wrong, and for the same reasons.

That breaks down the moment you encounter a culture with different values that you would consider 'deal-breakers'.