And the Crusaders slaughtering the non-Christian residents of cities in "the Holy Land" is no big deal?
From what I've been told, there were some rules about capturing cities back then. If you surrender right away when our army shows up, we'll treat you well. Close up and require us to do a siege, and we'll be a bit harsher when you run out of supplies and surrender.
Refuse to surrender at all, so that we have to storm the walls and take the city by force? Then you won't like what happens...
This was not some purely medieval thing, the ancient pagan Romans played by similar rules.
"Don't kill civilians" as a rule of war came later on... and sadly, did not really last long.
The "bad emperor problem" getting millions killed every three to five hundred years? It might be more frequent (I'm of the opinion that it's mostly just greater ability to be a dick, such as the Khmer Rouge's use of radio), but you're delusional if you think that the ancient philosophies and religions haven't created "hell on earth" for plenty.
We don't normally take things in South-East Asia into account when comparing Medieval Europe with the modern world, but what makes big-C Communism so murderous is its basic premise of "Burn it all down so that we can't build something better in its place!" The more ideologically "pure" the Communist group, the more of an extreme format-and-reinstall they will try to impose on the places they take over.
At a certain point, the blame has to be passed to the people who had nearly unquestioned moral authority for a dozen lifetimes straight for making a system without failsafes. The church had the opportunity to define everything about what was considered "right", and decided to make a completely all-or-nothing mass resting on God where before there was a variety of independent reasons, where any one thing rejected is equated to rejecting everything. The French Revolution is at least as much a Catholic failure as the modern CCP is a failing of Communism.
Well, there's more than one side to that. The RCC in the era of the 11th to 17th centuries was very much into making themselves the supreme authority over everyone else, with "because The Church says so!" as the final argument, and designing society so that it would all implode if people stopped believing in the authority of the pope would have been seen by them as a feature, not a bug.
But on the other hand, they also supported the philosophical tradition reflected by people like Thomas Aquinias, with his attempt to derive much of morality from natural premises and logical deduction.
The RCC's dogmatic prohibition of contraception, for example, has not a word of Biblical authority behind it. It's 100% Thomistic/Aristotelian.
Second example to go with mrttao's post. Just because Intersectional Wokists subvert all the institutions does not mean the ideals are unified. Between their struggle-sessions and the fact that the literal churches get subverted by them, they themselves do not support "all progressive ideas" and you can't pin the institutions position on whether they're atheist or not.
Marxist revolutionaries don't want to negotiate with you,
they want to kill you. Their demands being incoherent, unreasonable and mutually-exclusive to each other, with the goalposts being moved anytime it starts to look as if any of them might actually be granted, is intentional.
They are not agreement-capable with anything other than the outright destruction of civilization.
This is as true of the Intersectional Left and other such "Cultural Marxists" as it is of the Trotskyites or Maoists.
You can't get millions of people to believe in the exact same higher power pressing for the exact same behaviors, and this reality has caused Christianity to commit quite a number of bloodbaths in its history ever since canonization. The Massacre of the Latins in 1182 comes to mind, as do the Wars of Religion.
Because of the inevitability of doctrinal drift, moral relativism is the norm. Abrahamic absolutism is the outlier, and demonstrably dysfunctional.
Again I refer to the "bad emperor problem". Not an atheism thing, but a one-man-in-charge thing. Which the Papacy went far out of its way to establish as expected, directly contributing to the East-West Schism.
(and yes, I really did leave the three quote alerts untouched for over three weeks)
Treating the existence of anyone who does not believe exactly the same as oneself as a problem to be solved by violence will predictably lead to lots and lots of violence, yes. But contrary to what you claim, that's not an exclusively Abrahamic mindset, nor is it one that all followers of Abrahamic faiths buy into.
Consider the very example you gave - the Orthodox churches rejecting the demand by the leader of the Roman church that he be accepted not merely as one of the leaders of Christianity, but as the only one, as the One Pope To Rule Them All.
Lots of wars came as a result of that split, but to my knowledge of history, all of them from the Papist side. The other side merely defended themselves.
Mostly true also of the Reformation. Being a Roman Catholic in a Protestant country was far less likely to result in being killed for refusing to change your religion than would being a Protestant in a Roman Catholic country.