I was about to go off on your exceptions as being new in recorded history, when I figured out the antecedent you were trying to reference was whether they were detrimental or not. That is what I was talking about vis a vis Hinduism, that it effectively was not new in recorded history since the Vedas codified something far older that was already in common practice, not that it was not detrimental.
I'm prepared to grant that Jainism and Bahai are exceptionally not murderous. They're also very small groups, so it would be rather like trying to judge computer users based on the population that uses BeOS. They're wildly atypical of religious practice in the world.
And Daoism... whose Daoism? Daoism is frequently used interchangeably to denote either the philosophy of Laozi and his disciples or Chinese folk religion or both. The Boxer Rebellion was quite violent I assure you, and though frequently viewed through a political lens, the boxers were fundamentally a Daoist mystical sect. Far earlier characters like Zhang Yu did quite a lot of violence in the name of Daoism, and I'm sure there are others but I have only so much time to devote to obvious patterns.
Religions can't start killing until they reach a certain critical mass. The first stage is always persecution from the pre-existing majority, during which they usually preach peace and tolerance (surprise, surprise). Islam followed this curve very rapidly, and Mohammed wrote all sorts of nice, high-minded peace and love bullshit in the Quran while he was leading a persecuted minority in exile. It wasn't until he turned the tables and was leading Mecca itself that he started writing the "kill them where you find them" convert or die shit in the Quran. Christianity took more time to get to that point, but after the various councils of bishops started labeling heresies and stoning/burning/crucifying/beheading "heresiarchs" and their followers, that's when things began in earnest. Critical mass was reached, and killing could and did commence.
Oh, and 'the religion of women and slaves'? Please. I know that this was a derogatory phrase to the Romans that modern Christians think lionizes (snicker) them as progressive, but it's anachronistic fantasy. No less than half a dozen times in the New Testament alone is slavery endorsed and slaves commanded to serve their masters as though they were serving Christ himself. Women were explicitly barred from teaching men, and their second class status in society was not repudiated but reinforced by New Testament teachings. They were told not to ask questions in church but defer to their husbands' opinions, etc. etc. It's all there in black and white. Christianity in many ways became popular through ultimately conforming more and more to Greco-Roman norms and usurping its traditions and morals. If it had remained simply what Christ taught and didn't contain all the Pauline doctrines it probably wouldn't have been nearly as successful. All this syncretism aside, which is a far deeper and more complex topic, as soon as Christianity was accepted by Roman society after Constantine, it was open season to kill.
I'm not going to play more what-if games about history since if religion were not a component in human society history would necessarily be completely different from what it was. While there would be conquests of the Levant, as there were before any Abrahamic religious societies contested for it, there would be no "Crusades" because a) there would be no Islam b) there would be no "holy land" c) there would be no concept of a "holy war". Just war. And it would probably be over quickly and decisively, instead dragging on for generation after generation because of some concept of divine will.
And sure, other things kill besides religion, but religion is superfluous. There is nothing that religion does that cannot be done just as well by secular organizations. Removing religious motivations for killing would result in a net reduction of killings, even though killings would still happen for other reasons.
And while I know you're being facetious, freedom, democracy, security and whatnot, but there's a real point there. These sorts of abstract concepts can result in killings, but they do not, as a matter of logical imperative, cause killings. There is not an inherent logical path of 'freedom... therefore kill' or 'democracy ... therefore kill'. A democracy can decide amongst itself that a person or persons should be killed, but they're not killed because of democracy but rather some other motivation which catalyzed the use of the democratic process to arrive at a consensus about the matter. Religions create logical imperatives, the Quran 9:5 says '[...] slay the idolaters wherever ye find them, and take them (captive), and besiege them, and prepare for them each ambush.[...]" the only way you can be a "true" Muslim is to follow the Quran, and the only way to follow the Quran is to kill people. It is a divine command, an imperative that must be acted upon without thought or doubt or there will be eternal consequences. It is evil, evil nonsense. (Christianity has something similar which Dominionists use as their license to kill, Luke 19:27 "But those mine enemies, which would not that I should reign over them, bring hither, and slay them before me." which granted is from a parable, but the allusion is to Yahweh, and try telling Dominionists 'it's just a parable')
Lastly, the Taiping Rebellion has more to teach than I think you're willing to learn. The Taiping Rebellion failed because it was religious. Many Chinese wanted to revolt against the Qing since it was a foreign occupation that had terrorized Han people (e.g. the que order), albeit with a significant Han collaboration. The Taiping Rebellion lost steam because a) the leadership were complete whackadoodles as is common among messianic movements b) the religious foundation was ostensibly foreign and had limited appeal among the broader Chinese society as a replacement for a foreign occupation, indeed it was a testament to their desperation that as many signed on as did, but I think a lot of them just saw it as a vehicle for change c) the movement was seen as untrustworthy and hypocritical because it preached morality and virtue but acted out debauchery. The corollaries to these things should be obvious a) if the leadership were practical, disciplined and prudent b) if the motivating vision was native rather than foreign c) if the actions of the movement were consistent with its message then the Taiping Rebellion would probably have been called something else and would also have been successful in establishing a domestic Han Chinese dynasty (which is what most of them wanted anyway).