That’s not true. Animal husbandry was not meaningfully present in primitive communism until it became the end of it. Agrarian/pastoral society is the foundation of most class society throughout the world, and the traditional Marxist account is that in Europe it produced patriarchy because “estates” of a sort are now in existence and systems wherein women were obliged to only have sex with one man in order to be sure of whose the child was became important for inheritance, and maybe more importantly fields and pastures made having more workers a much more economically valuable thing than in a hunter/gatherer situation, which means that you want more reproduction, which resulted in women being forced to reproduce more and even women being kidnapped from other tribes in order to have more people producing future workers, so now women are a brutally-oppressed underclass ruled by the patriarchs.

Religion existed in primitive communism and throughout human history thereafter and was never the origination of a class divide even if it would go on to be useful for perpetuating class relations (as all ideology is used to perpetuate class relations). We should not be so over-zealously anti-religious that we fall into idealist explanations that blame religion when one of the most basic pitches of this community is that religiosity interferes with materialist analysis. Class divides originate from material conditions, religion supportive of class divides comes after, as the ruling ideology developed by the new ruling class.

Edit: Engels covers a version of this in Origin of the Family, Private Property, and the State, and here’s an audiobook that I quickly found, but you can probably find others if you don’t like this one.