In a better world, no one would be transgender.
Let me back up a little here. What makes a person transgender? I recently wrote a simple definition:
Does your gender identity and/or expression fall outside the bounds prescribed by your society? You are transgender.
This is a commonsense and widely accepted definition. For example, the National Center for Transgender Equality writes (pdf):
Transgender: A term for people whose gender identity, expression or behavior is different from those typically associated with their assigned sex at birth.
So transgender does not describe the state of having a particular combination of physical and psychological traits (e.g., being a woman with XY chromosomes). Nor does it describe a particular gender identity (e.g., a person who is neither a man nor a woman). Transgender describes a sociopolitical location. Transgender people are those whose genders are taboo.
In a better world, all people would be free to inhabit their bodies with dignity. No one would be ridiculed, assaulted or killed for being too feminine, too masculine or too androgynous. No one would be the target of interpersonal and institutional violence because they have an atypical body or gender expression. Therefore: no one would be transgender.
Now, so long as there are men and women, there would still be men born with ovaries and women born with testes. There would still be androgynous, agender and other nonbinary people. There would still be statistically rare combinations of physical sex, subconscious sex, gender expression and sexual orientation, including those people we now call transgender, intersex, genderqueer, gay/lesbian/bisexual and asexual.
But transgender is a state of systemic marginalization. To be different and not marginalized is an experience almost unimaginable today. If we were not targeted for our difference, it might mean very little, and certainly something very different. Maybe being transgender would be a bit like being left-handed, having an allergy or having perfect pitch.
Are people who inhabit 3rd, 4th and other genders, in societies that honor them, “transgender”? Would we be “transgender” if the wrong gender had never been imposed on us? If we were never exiled, there would be no journey to make, no border to cross, nothing to transgress, transition or transform. Some people would still utilize hormones and surgery. But without cissexism, that might be a bit like, well, utilizing hormones and surgery is for cisgender people (hormonal birth control, surgery for gynecomastia, etc).
In other words, we would probably still have genders. But we wouldn’t be trans anymore.