Though I agree mostly with a) and c) and noticed you no longer consider shaman to be associated with evil, so I can generally agree with your first three points, I am still surprised that lizardmen, stone giants and quaggoth are considered "violent" and "primitive" and I'll try to make the point that b) is already implemented in the monster manual.
The stone giant are described this way: "Stone Giants are reclusive, quiet, and peaceful as long as they are left alone [...] They are private creatures, hiding their lives and art away from the world". Later "Stone giants view the world outside their underground homes as realms of dreams [...] Killing prey or sentient beings is no cause for guilt in the dreaming world beneath the sky." and finally "When trespassers stray too far into the mountain territory of a stone giant clan, those guardians greet them with hurled rocks and showers of splintered stones. Survivors of such encounters spread tales of stone giants violence, never realizing how little those brutes dwelling in the unreal dreaming world resemble their quiet and artistic kin".
So, they carve exquisite art, have advanced stoneworking and masonry techniques that surpasses the dwarfs. There is nothing "primitive" implied in their description, except that they throw rock boulders as a weapon, but catapults do that as well. Basically they didn't need to devise more efficient weapons. They do have an alien view on the surface world, but the only manifestation of violence is against "trespassers" who "stray too far" into their territories. I am not sure the human cultures usually depicted in D&D settings are less violent than that. Think of Eberron: the five main nations had a bloody 100 yaars wars for... succession. They attacked each other because some guy or gal sitting on the local throne wanted to grab his cousins's throne. And these cultures should be lecturing stone giants who just want trespassers to let them alone? I don't think we should hold them to a greater standard of peacefulness than other fantasy cultures. And for those who say that "being in a fantasy isn't an argument", I could add that some real life cultures, among which D&D is sold, fully supports a real life personn who'd shoot at intruders trespassing into his home. Most cultures where D&D is sold would support defensive wars. Interestingly, stone giant are mostly, in setting, victim of prejudice, since the surviving trespassers (ie, bad guys) "spread tales of stone giant violence". Their brutality is only self defence, granted they might show little pity to trespassers, but who would? Apparently, adventuring groups usually don't have a sense of guilt when they kill bandits, so they are not different from stone giants on this account, despite not sharing the alien giant worldview of the surface world.
Basically, shamans are associated with a peaceful, culturally evolved group of giants, who might even be less violent than the default (human/elves/dwarves) and they are prejudiced against because of tales spread by the default (human/elves/dwarves)...
Same with lizardfolk, they are primitive, but not especially violent. It is only when their shamans jobs are usurped by followers of Ssessinek that "these lizard kings and queens dominate lizardfolk tribes, usurping a shaman's authority and inspiring uncharacteristic aggression among their subjects". They are only violent, like stone giant, when their territory is invaded. Agression is "uncharacteristic" to them. They happen to eat anyone who trespass, making "no distinction between humanoids, beasts and monsters". So, they are omnivorous, big deal! Same, when an evil dragon exploit them, they are turned into "raiders and plunderers". So basically, barring outside, evil, influence, they are just wanting to be left alone. They don't seem to be any more violent than the default. Primitive, yes, alien in their worldview, yes, but violent? Not really.
Interestingly, they are also victims of prejudice (the merchant account above the lizard king stat block, for example) and the (previous edition) blurb about their flesh eating habit. It's easy to suppose that the survivor of a trespassing expedition would spread distorted tales of cannibalism, as in "they all want to eat human flesh" and not "they are omnivorous, including mammal humanoid flesh".
Granted, quaggoth are primitive AND violent. I could make the argument that shaman are associated with one violent culture, one peaceful culture and a neutral culture, so they are associated with the whole spectrum violence-wise. But let's continue and explore the source of this violent culture. The fluff tells us that "Quaggoths were never an enlightened species" (ok, they are primitive) "but they were not always the brutal Underdark denizens they are today. In a distant age, quaggoth tribes dwelled upon the surface as nocturnal arboreal hunters, possessing their own language and culture". Really? So they were more advanced, despite not being "enlightened". OK. What happened? "When elves appeared in the mortal realm, they clashed with the quaggoths, eventually driving them to near extinction". WHAT?!? Elves committed a genocide against a sentient , intelligent, species with a language and culture? I hope they are not setting the standard for morality in the game! And they call the not Quaggoth "not enlightened"? "Only by fleeing deep into the Underdark did the quaggoth survive". Not "into the Underdark" but "deep into the Underdark". Apparentely, the genocidal war against the Quaggoth wasn't just a need for the elves to acquire a territory (since they arrived later and wanted to take some place to live) but they chased them even in the outskirts of the underdark to make them extinct. "Weird magic of their new realm transformed them. Turning increasingly brutal and savage, they ate whatever food they could find -- and when they could not find it, they preyed on each other. As cannibalism became part of their culture, their past was abandonned". So basically, they had to turn to sustenance cannibalism and were subsequently even more transformed by the dark elves.
In this third, and final example of refence to a culture with shamans, we do have a primitive and violent culture, but it is made explicitely clear that they are in this sorry state because of the genocide conducted by the elves in the distant past, and had to live in the equivalent of a radiation zone. The prejudice against them was immense, to the point of them being killed, all of them, even the baby quaggoths, despite them not being evil, even in their current state.
So in the current 5e MM, shamans are associated with:
Evil Alignment ? 0 case out of 3 (as was shown previously).
Violent ? 1 case out of 3, with a fluff explaining that their inherent violence is the result of being extremely brutalized in the past by a player race and wild magics, and that they had shamans before, when they were not yet violent.
Primitive? 2 cases out of 3.
Prejudiced against by the default setting races ? 3 cases out of 3.
I agree that they could make more explicit the fact that non primitive cultures (ie, metalworking and living in an environment were complex, far ranging social organization beyond the clan level are needed) also have shamans to avoid misconception.
I do like, however, that stone giants, lizardfolks and quaggoth, all who have shamans, are the victim of prejudice by the cultures the players usually hail from. I feel some can share some of this prejudice "surely, they must be evil, they are CANNIBALS" without considering the origin of this cultural trait (not being a mammal in one case, being forced into it for sustenance reasons in the other) or "they are violent, they throw ROCKS at passer-bys" without considering the self-defense aspect of it and the fact they wouldn't, as PCs, behave differently or "they are primitive, they don't USE METAL TOOLS" without considering that maybe you can have exquisite culture that just happen to not follow the same steps as yours. In exploring the setting, they can realize that the reality is more nuanced, more complex, and that their own approach was judgemental and misguided. It prompts reflection over the player's own values in case he shares some of this prejudice. In setting, if we keep shaman as the religious intermediary of the victims of prejudice, it's easy to include this particular prejudice into the regular PC cultures ("look, they are evil worshippers, they have shaman and not proper clerics") to add another avenue of reflection on whether the PC culture is really in a position to pass judgement over them -- perhaps one more easily acccessible to players, because they will easily realize that shamans aren't inferior to priests, while they may struggle at first with recognizing the other source of prejudice (it's easy not to realize that the violence you're recieving is justified, or to think that cannibalism is inherently evil when our own culture has a cannibalism taboo). If you make shaman more culturally widespread, you remove this particular proof of prejudice by the default culture, but you don't really substract to this trend because there are enough proof of it in the remaining fluff.