There's a lot of Atheists who still follow moral laws
Then I'll disagree with you that they are atheists. If they believe in morality they believe in a Higher Being. "All men are created equal in the eyes of G-d." Tale away the last part of that sentence and you're left with a "says who?". We don't look like we were created equal. If we are all just another species of animals then just like animals, the strongest (richest/smartest/whitest, etc.) one gets his way.
Now here's how your question is a issue: By saying Morality is dependent on religion what your doing is assuming that the laws we have in place in society are only there (Most people consider the laws we have in place as moral - it's illegal to kill in US law and the Torah) and we consider these things 'normal' and thus why when we see people like ISIS and what there doing as 'barbaric'.
Anyhow the big question you pose --Brings us to this---> is our laws based on the Bible/Torah - (Old Testament-How ever you flavor it)-many will say though that it's just known that you shouldn't "Kill" steal, rape.
Looking at ancient civilizations (or indeed the idea of a civilization as opposed to a nomadic tribe), you see that it wasn't "known." It was an idea that had to be introduced to humanity. The Torah was the one that introduced morals to the world.
So it brings us to a huge philosophical question: What really makes what's shown in the Bible "Moral"...as Jews or people we have alot of issues in our religion that we debate and discuss but everyone can agree that certain things are just true. Its wrong to Kill for no reason, Steal, Rape.
Again, these have been accepted as cultural truths. But- why is it wrong to steal or rape. I want that. I'm stronger, I could grab it away- so therefore, I should have it. It is only the idea that we all have equal rights to life, to our possessions (because we were created equal in the eys of G-d) that changes things.
Which gets me to the actual question: Is what G-d says is moral, moral because G-d says it or is it Moral independently and G-d says it. -- Is murder wrong because G-d tells us not to do it or does G-d tell us not to it because it is wrong.
Yes, I've heard that one. It's right up there with the big questions along with "Can G-d create a stone too heavy for him to lift?"
The answer: As a Jew, I believe first (if there can even be a concept of first or later before the creation of time) there was G-d. G-d decides it's good to be good and bad to be bad. He decides what is good and what is bad. (I think that's the order...) He lets us know what is good and what is bad in the Torah.
If you can envision the notion of Morality before god, that morality exists and therefore god desires it- then what is your god worth?
Your second point of the "Law Of the Jungle" which I assume is a phrase to do what ever you want --> but societies have always set up laws...you can bring me points about ISIS and other groups who ARE doing what they want -- killing, raping...and they do it under a "Religion"...but to be fair they are just perverting the ISLAM religion.
Societies have also set up religions- but that is irrelevent. A society setting up laws in order for it to be able to function isn't acting on behalf of morality. If I don't steal from you just so that you won't steal me- that is just selfish. Not moral.
Attached is the literature supplied by my Atheist Ethics professor when we broached this topic. Almost all of the arguments I presented I believe can be refuted . . . personally I disagree with a lot of what's mentioned in the text, including my arguments above...Im just playing devils advocate.
Too small to read. Maybe I'm getting old.