Yes, all revealed religions are based on the authority of revelation. But you are wrong to say that something isn't wrong because it causes harm. What revelation does is define what constitutes 'harm.'
Except that, for the most part, it does not.
"God said it. That settles it. Case closed."
Any line of reasoning that'd put the evaluation of harm at the centre of moral considerations is not theistic in nature, because it's not about a deity or a deity's commandments, but just about an analysis of interpersonal relationships - or about even more fundamental social emotions.
Actually most of the prohibitions (though admittedly not all) are there because they doing them does cause harm.
But the pertinent question here is: what came first? The realization that certain actions cause harm - or attributing them to a deity? Judging by the social behaviour of other species such as wolves, apes, or elephants, I'd say that these moral impulses precede the advent of religion by at LEAST one evolutionary step towards the development of sapience and culture.
And yet the atheistic ideologies which have come to govern have oftentimes caused even greater atrocities.
I'm surprised to see a highly educated person like yourself repeat this rather polemic and somewhat ill-founded argument.
First and foremost, the problem with the -isms of the twentieth century was not that they were (in some cases only supposedly) atheistic, but that they were TOO MUCH LIKE a religion. Communism (and its mirrored twin, Randian Objectivism) have their own eschatology, a sense of mission, a clear compartmentalization of the world into the "good" in-group and the "evil" outsiders, and - last but not least - an unquestioning belief in the authority of the "Revelation".
Secondly, I'd say technological progress accounts for the huge number of casualties much more than the nature of the ideologies involved in the various conflicts. Counting deaths and declaring the party with the smaller body count the morally superior winner does not even make sense when both situations involved the same technology and the same population size. But given that we are comparing people with spears to people with poison gas (and at a time when the global population was significantly larger), it is even more nonsensical.
Last but not least, the often-cited worst offender in this regard (namely the Nazis and the holocaust) weren't even predominantly atheists, and their ideology was building on a millennia-old tradition of anti-semitism that had been perpetuated by Christianity since late antiquity.
Do they? I see a lot of atheistic philosophies such as Ayn Rand that make a virtue out of selfishness.
"Objectivism" is very much an atheistic religion, including its own eschatology, the repulsion of "heretics", lists of prohibited books, a scriptural canon, etc.
And of course, you kind of missed the point here. Objectivism is not "empathy and sympathy on their own", it's the diametrical opposite - the same mechanism that I also described in relation to theistic religions.
I'll grant you that being a theist and being moral are not the same thing, nor is atheism necessarily immoral. But I think oftentimes that even when atheists has eschewed religion, they often draw on the reservoir of moral principles which religion established.
The thing is, though:
"religion" did not establish anything of the sort. I mentioned the other social mammals before: our ability to relate to others and to act morally based on these emotions and thoughts precedes the advent of culture (and thus, by extension, religion), as does a group's outrage at seeing an individual do wrong, or an individual's guilt at acting in an anti-social manner.
Social instincts are not fool-proof, of course, neither collectively nor individually. The lynch mob, the de-humanization of the out-group, pecking orders - even despots: all side effects of certain behavioural patterns that have been deeply ingrained into our collective psyche, only to be overcome by reflection, reasoning, discussion, learning.
Culture (theistic or not) *can* aid in that process, in theory.
Historically speaking, however, it was more often a hindrance rather than a help. Christianity systematically resisted and blocked any kind of social progress throughout history - yet retroactively claimed that it had been the driving force behind the change afterwards, pointing at a few mavericks who had re-interpreted their stance in a highly unorthodox manner.
The advantage I see in a non-authoritarian culture is that it is significantly more open to debate, to well-reasoned lines of argument, to a questioning of tradition and established practices - in short: to change. Once you point to a text and claim that this is the Supreme Being's indisputable Will, that option flies straight out of the window.