So, if we weren't socialized into our gender, it's quite possible we'd act as neutrums..?
Not as such, no- the evidence seems to suggest that each biological sex (setting aside intersex people for a minute) have certain general tendencies, but the key is that these are individual, and that gender- among other things- limits individual realisation of
personal identity. It's quite probable that, in a genderless world, most men would act in a recognisably "masculine" fashion, and most women in a recognisably "feminine" fashion. but this would be an individual choice, and no prescriptions would be made as to behaviour deemed "proper" for one who happens to possess a certain set of reproductive organs.
Remember, "gender neutrality" is a gendered concept in itself, in that it exists as a mid-point between two traditional norms. Without these norms, there can be no mid-point, and so no meaningful concept of "gender neutrality".
..and the "trans-, third, inter-, bi- and agender"ed people have been mostly socialized into thinking they're of a gender different from what's most common?! ...or their perception of being what they believe they are is irrelevant because the genderroles are just a social construct?! It's a bit disrespecting toward HBT-people.
It's more complicated than that; gender is a construct, but that does not delegitimatise a gender expression within the terms of that construct, either cis or trans, if that is what gives any individual feels comfortable doing; "construct" does not mean "bad", after all. It's simply important to remember that it
is ultimately a construct, and so not everyone will necessarily feel that adhering to it's terms is fulfilling for them as an individual, and so may opt for an alternate form of expression, such as agenderism, inter- and third genderism or bi/polygenderism. (The distinction between a-, inter- and third-genderism is not very precise, and is often simply a case of individual identity. Bi/polygenderism refers to a person who entertains multiple gender identities- discreet or fluid- depending on mood or circumstance.)
It should also be noted that there is a distinction between transexuality and transgenderism (although the former almost always entails the latter). The former is properly understood as an intersex condition which makes it difficult or impossible for an individual to identify with the anatomy they were born with, while the latter refers to any non-conventional expression of gender. In a genderless society, the latter would cease to exist in a meaningful sense, as there would be no convention to deviate from, while the latter would still exist as a psychological and medical concern.
Or maybe our gender, what we feel we are, only can be expressed through acts that are associated to the specific gender and will never vanish even if they'll appear in different forms.
As I said, it's certainly true that, for the majority, their natural tendencies are towards something vaguely approximate to gendered behaviour, but this is far from universal, nor, it can be argued, would the natural tendency of the majority conform to the limiting and rather exaggerated norms presented by the traditional binary.
