With regards to the topic of genders (and the relationship to biological sex), the overwhelming majority of societies throughout history (both from varying religions -both monotheistic and polytheistic-, and from secular ones) all seemed to drift toward those similar conclusions despite not collaborating with each other.
I think you're ignoring the possibility that some "social constructs" can and do exist for reasons pertaining to lived experiences and observation of the natural world, and aren't exclusively the result of religious indoctrination.
I would take it one step further and say that it's not conjecture or a mere possibility that this is the case, but reveals something very deep about the cross-cultural conceptual organization of information in the human brain. When I was in grad school for my master's degree in Linguistics, one of the really important classes I took was with the great Dr. William Croft, a linguist who has published his very important work "Radical Construction Grammar: Syntactic Theory in Typological Perspective" with Oxford in 2001. While I never owned a copy of the book in question, the class he taught on the subject made the point (among many others) that there is a sort of 'animacy hierarchy' involved in the grammatical 'sexing' of animates, cross-linguistically (that is to say, around the world, in a myriad of different cultures). This animacy hierarchy explains not only why it is vastly more common to find sexed terms for cattle than for mosquitos (hint: it has to do with who is naming things in the first place), but also very important distinctions that humans make around the world regarding
human beings -- i.e., why we have terms for man and woman, often for young man and young woman, also often for boy and girl, but much less often for 'male baby' and 'female baby'. This is what Dr. Croft referred to as the "neuter baby phenomenon", and it is indeed something that we found to be true around the world: because there is really no pressing reason to distinguish a male baby from a female baby in the vast majority of situations (it doesn't 'mean' anything for the tribe or the society), plenty of languages around the world just don't have terms for that. Your baby is just a baby, until it becomes reasonable to begin referring to it as a boy or a girl some years down the line. Note that none of this denies the
biological reality of male and female babies. It is purely about what linguistic forms are found or not found around the world, and why.
On a personal level, because the above is a part of my academic background, when I look at all of this trans/multigender stuff, it is through this sort of lens. I am constantly asking myself "What conceptual space is being created here via this particular use of language, and towards what end?" The 'bias', if you will, towards a binarily-sexed world, if not entirely uncomplicated by several factors (e.g., intersexed people, various other conceptions of human gender in different societies around the world), is at least
explainable with reference to the actual world in which we all live, regardless of how many genders of human being we think there are. This is why it is argued that this represents something deep about the organization of information in the brain: not because this is necessarily a matter of clean and discrete categorization or compartmentalization (the animacy hierarchy is more of a spectrum than a scale), but because the same patterns are found over and over again in a myriad of distinct cultures around the world who have had no real contact with each other, and hence cannot be assumed to be influenced by one another, or all embracing a similar religious or cultural worldview that might help explain what we see crop up again and again in linguistic structures found around the world.