Atheism is just an absence of belief in gods. Nothing to do with "objective morality" or any kind of morality.
I Know that is why I said objective morality can be compatible with an atheist but it can't be found within atheism.
Theism doesn't have anything to do with "objective morality" either.
Yes it does, God's eternal nature determines what is right or wrong, what has value or none, what rights are, if any actual equality exists. It is not a mater of opinion, not even God's and is there for objective. There cannot be a more objective source possible than God. If you have concocted a semantic technicality to claim he is not objective then the word no longer has any meaning.
Theism is just a belief in god(s).Theist or atheist doesn't matter, we both evolved a survival instinct. So nature by way of evolution and natural selection programmed us to see survival as "inherently right by nature" and non-survival "inherently wrong by nature". Which is why we instinctively run out of the way of an oncoming car. We don't run out of the way of an oncoming car because some regulations say we should but do it instinctively because the act is "inherently right by nature." Acting in accordance with the Golden Rule is "inherently right by nature" because it enhances our chances of survival.
Survival of one species (namely us) at the expense of all other life forms on the planet is not moral, it is selfish speciesm. However whatever it is, it is impossible that it is an objective moral. Nature does not contain one atom with a moral property, it is 100% amoral, and it can never tell a single being what it 'should do". That does not mean humans cannot invent subjective ethics and call that morality, but it isn't morally objectively true. We ruin out of the way of a car because we not want to be hit, but what we want cannot produce a single objective moral fact.
I have never understood why non-theists take a bible with several thousand moral duties in it and reduce it down to the Golden rule.