What's the name of the fallacy of the form 'You're wrong about X, therefore you're wrong about Y'?

I'm a huge fan of Dr Jordan Peterson's work. However, I disagree with him n the issue of religion; he appears to believe that acting morally is a sign of (unconscious) belief and atheists aren't really atheists. I've seen some people trying to attack Dr Peterson along the lines of 'He is wrong about atheists' beliefs, therefore I dismiss everything he says'. So, the fallacy, as I see it, runs thus: If he is wrong about X, then he is wrong about Y and Z'. What is the name for this?

"My understanding of Peterson is that he is making a case that claims you can no longer say morality would still exist without religion. Under pinning morality is centuries of religious moral teaching. To simply remove all religion today would not make the point that morality exists without religion, for religion has already been your school master."

The natural sciences of behavioral psychology, anthropology, archaeology, ethnology, mythology, evolutionary psychology, and neuroscience prove that morality develops from the evolving human nervous system and predates all the formal belief structures and civilizations going back to the earliest sapient beings. Certain Simian species exhibit empathetiic, ritualistic, and instinctual behaviors that resemble expressions of dance, music, and ritual very similiar to primitive human cultures.

The term Religion itself is problematic because it assumes a supernatural relationship with a divine other. Its Latin root religare is the same as ligament and means to bind with a divine source. If Peterson is suggesting that morality comes from a divine or any other source than the human brain than he is woefully off in woo woo land. There is consiiderable evidence to show that Neanderthal's developed a complex system of rituals and beliefs based on the primitive idea that "Life Comes From Death" and even developed a religious code around the capturing, nurturing, worship and ultimate slaughter of bears in religios ritual. Their religious belief developed from their sustenance, nourshment and very survival on their dependent upon these creatures whom they considered other worldly, if not divine. Sure, it could be said that their morality of gratitude came from a natural awe and revery, but it is more of a case of a religious belief system forming from an innate moral balance within the human imagination. Early man believed (supernaturally) that Life comes from Death, and therefore to create more life there must be more death." (See Ellis Polynesian Researches, A.R. Radcliffe Brown’s The Andaman Islanders and many many more). I have to run an errand or would offer more citations.

'He is wrong about atheists' beliefs, therefore I dismiss everything he says'.

Part to whole fallacy (also Genetic Fallacy)

"acting morally is a sign of (unconscious) belief

The operative word here is "unconscious". Certainly, some behaviors might be unconscious (genetic, pathological, programmed, etc) but others perfectly conscious. So it is a false premise or at least an irrelevant thesis. It might be worthy of a different discussion, but here it is a distraction.

The general consensus of neuroscience, behavioral science, and evolutionary psychology is that morality is simply a form of conformity ( Havelock Ellis)

The current perspective on morality and misbelief is from a by-product perspective as side-effects of a suite of cognitive mechanisms adapted for other purposes ( see Dennett and McKay) Humans have open nervous systems and can be morally programmed by both genetics, traditions, and culture. (Bettleheim, Frobenius, Jung, Lorenz, etc)
.
Atheists aren't really atheists. Opinion,

It could just as easily be claimed that theists aren't really theists because much of their moral beliefs are not only programmed but possibly contracted through viral ideologies, identity politics, or under ad baculum duress. ( see Pascal's wager)

Ultimately, atheism makes no claim as a moral system, whereas religion is by definition a moral system - a path of beliefs and behaviors designed to reunite one with God - (Latin religare ‘to bind.’) Of course, religionists claim it is atheism is an amoral system, but then again to the religious hammer, every problem is a religious nail.

My understanding of Peterson is that he is making a case that claims you can no longer say morality would still exist without religion. Under pinning morality is centuries of religious moral teaching. To simply remove all religion today would not make the point that morality exists without religion, for religion has already been your school master.
This is similar to, if not exactly the same as the Christian Argument from Morality for the existence of God.
As you say, “atheism makes no claim as a moral system”, I agree.
What system would emerge without religion? Probably no different than those that rose out Communism and Nazism. Would an atheist call such systems “moral”? If so, how so, since it makes no claim as a moral system. It has to borrow from religion. Evidence according to Peterson, that there may well be a God.
Is there a fallacy there?

Poring through the pained and painful pleadings of the Christian fundamentalists who haplessly and to some extent disingenuously wander into these threads, I am reminded of just how dangerous and delusional belief systems can be.

The irony is that the delusion is not so much what they believe, however nonsensical or paralogical, but the strenuous effort of pseudoscience, pseudo historic metamorphosis (Spengler), Paiduma (Frobenius), revisionism, apologetics, suspension of disbelief (Coleridge) and mindless memoriter they must indulge mantra-like to maintain it.

I'm reminded of a quote from one of favorite screenwriter and authors Sir Robert Oxton Bolt who said, "A belief is not an idea the mind possesses, but an idea that possesses the mind." Of course, he wrote this long before we started identifying the neuroscientific phenomenon of ideological brain viruses (good and bad) and how quickly they can infect an otherwise healthy, modern civilization. Of course, the apologists and Christian revisionists love to point to Communism and Naziism as immorally atheistic ideologies, while conveniently excluding Early Catholicism from their survey. Unfortunately, this foundational bias ignored the fact that all three began as highly developed moral systems before they degraded into monstrous genocidal regimes. The sad reality is that some of the greatest ills, wars and genocides deveoped from so-called moral misbeliefs.

Mikhail Sergeyevich Gorbachev often attempted to explain Communism as an economic and social version of Christianity.
Naziism developed out of centuries and centuries of Biblically based anti-Semitism from the very pages of the New Testament. Jews were not just considered Christ killers, but baby killers and spreaders of pestilence, disease and natural disasters. Indeed, if we remove the absurd theological spin we have every right to question what religion of peace would choose as its most sacred symbol, as George Carlin used to describe, as a "dead Jew on a stick"?

Yet, the origins of what would turn into malignantly immoral Nazis creed developed from an exceedingly "moral" quest for a Pan Germanic mythological ideal (See The Grimm Brothers) that sought a native mythos of the German people that was not rooted in or mired down in an Abrahamic tradition, Catholic catachism, or fanatical Protestantism. What developed into Nazism was a malignant genocidal hybrid of both Christian dominionism and rabid nationalism that held Race and Law over all other human values. Ultimately, Catholicism, Protestantism, Communism and Nazisim had very similar goals. One cannot separate the Nazi death camps from the murderous campaigns of Constantine, Justianian and Theodosus, or the genocidal "moral" purges of paganism, witch burnings and inquisitions of the 16th and 18th Centuries. They were all arguably moral efforts corrupted and turned malignantly immoral. ( (See Gibbon's Decline and Fall of the Roman Empire, G W Foote & J M Wheeler's Crimes of Christianity, or Der Untergang des Abendlandes) The Downfall of the Occident, Spengler