I do wonder how the Amaloxians (neo- post- or whathaveyou) would view gender nonconforming individuals or how their gender-based ideology would view our conceptions of transgender people. I believe that some ancient cultures had specific religious roles for third gender individuals, perhaps the Amaloxians could have developed some analogous role?
I'll split this up into several sub-topics:
Gender and the Danubian cultures
Looking at the Danubian culture, which is unchanged from OTL until later in the 5th millennium BCE, we must concede that we know almost nothing about their gender concepts, in spite of the heated controversy which unfolded in the last century over Gimbutas's theory. In this respect, the Danubians are not much different to us from other Neolithic cultures.
John Robb has concluded in his overview on Neolithic European archaeology that gender roles may not have been quite as rigid as they were in the Bronze Age. That may have been the case - but it's no safe ground to speculate on transgender attitudes from.
Gender and TTL's Archaic, Classical and Post-Classical Amaloxian society
Now, ITTL I have committed myself to the Danubian culture espousing female clan elders from the 5th millennium onwards, and throughout the 4th millennium slowly concentrating more and more power in female hands, a process which is only concluded into a rigid matriarchy in the Classical period (from 2750 BCE onwards). That means, throughout the Archaic Period (most of the 4th millennium) and the First Intermediary Period (end of 4th and beginning of 3rd millennium), things are still more in flux. But that primarily concerns the question to what extent power is gendered as female, it doesn't really say anything about transgender individuals and how they are viewed. Specific religious roles for third gender individuals, like certain Assyrian dancers or in quite a few Native American traditions, are really possible only before the Archaic state of Kalazza imposes its structure on other Amaloxian polities, i.e. until the first centuries of the 4th millennium, and then probably for a while during the First Intermediary Period. Because the Archaic and Classical Amaloxian states are theocracies, built on nine female priestesses holding supreme power, and subordinate priestesses serving similar roles in the territory, each of them tasked with a specific domain, but celebrating certain most holy rituals together. From among them, Xušrax and Pilušvil are the ones tasked with dealing with male deities, but if that makes them more likely to be defined as strictly female or less so is something I couldn't decide. Overall, the priestly caste, who hold the highest power in the state, are probably the least likely spot for gender-crossing, and at least in the Classical period, there are no other religious figures left anywhere in Amaloxia.
In the post-classical period, priestesses are no longer the most powerful people, but their traditions are likely to only harden because of that. So, no religious roles for transgender people in Amaloxia.
Another thing I considered but rejected is whether male soldiers, who still existed in the Archaic period, would be castrated. It would make sense to the Amaloxian female elite on the one hand (to put it in their spiritual terms: they wouldn't scare Apashung so much), but common consequences of castration (listlessness, obesity, depression) don't make for good soldiers, so no eunuch army, either.
What about other roles? Now, I believe that there are people, whom we would identify as transgender, in any society at any time - every human culture develops gender roles of some sort, and every human culture has a few people who don't fit in or don't stay on just one side. Here, we need to consider what these cultural gender concepts in Amaloxia stretch to encompass. While I'm at it, I'll also address prevalent Amaloxian views regarding homo- and bisexual practices and preferences.
In Archaic and Classical Amaloxia, and to some extent also in Post-Classical Amaloxia, as far as we can speak of their culture as homogeneous (which oversimplifies things of course), women are - stereotypically; I wouldn't think everyone would subscribe to this, but as a general description of cultural models it works - ascribed superior wisdom and responsibile behavior, social competencies, proximity to the goddess of life's balance, being burdened with the difficult decisions and the cabbals of power. Men, on the other hand, are stereotypically ascribed raw and uncivilised natural power, vagrancy, impulsivity, and a proximity to animal spirits. Therefore, cultural transgressions of gender roles could sometimes be associated with performing what is stereotypically ascribed to the other gender: women dressing as men are not unlikely to perform what would be viewed as living out wild impulsivity, or dwelling among certain animals, or testing their bodily strength (e.g. in wrestling) - this is likely looked down upon by many other women and relegated to the fringe of cultural behaviors, but not necessarily penalised -; on the other hand, men dressing or posing as women is likely to be very explicitly ruled out, until perhaps later among the Neo-Amaloxians, where successful male exceptions among the leadership might well take on (or be ascribed) features culturally marked as female in order to make their holding of power appear less exceptional.
Homosexual practices are not likely to be culturally ostracised, neither among women, nor among men. Among the "fighter nuns" of Classical Amaloxia, especially in Šukhtityar and other large towns, they're likely to even be normal. Male gay practices are likely to be largely ignored and at the same time they're probably the stuff of raunchier kinds of cultural representations shared among the literate female elite. Note that I spoke of "practices" - DEFINING yourself as lesbian or gay or bisexual is less likely to be openly accepted, especially in rural communities, but there is always the mantle of female priestly "celibacy" or male "dwelling in the wilderness" to escape the standard female-male monogamous relationship norm and acquire some leeway.
Permanently not committing oneself to one gender is not something that's going to work well, which is also bad news for biologically intersexual people (although probably not worse than OTL, either), since they'd be placed outside of the gendered asymmetrical social roles of both urban and rural Amaloxia, and in the worst case even outside of the clan structure. Being neither man nor woman (or both) is probably the only thing that's worse than clearly being a man in Amaloxia from classical times onwards. (There may have been some loopholes in Archaic and First Intermediary Period times.)
Indigenous Tanayan groups today and their views on gender
This could go either way. On the one hand, to maintain their distinct traditions over such a long time they need to be very culturally conservative. On the other hand, when Ethnicist thinking has subsided ITTL, too, there may be increased cultural exchange iTTL's modern age, and post-Amaloxian individuals could just as well be among the leading icons of gender-reflexive theory and praxis, including transgender issues.
Classical Amaloxians ISOTed to OTL's present - How would they view our concepts of transgender people?
Utter culture shock is guaranteed anyway. Individual reactions are bound to vary greatly after that. (That is a cop-out, I know.)
. But of course, I wouldn't ask you to flesh out too much about them, that's quite a lot of work!