“Transgender,” sometimes truncated to simply “trans,” is an adjective. To illustrate some of the more, erm, peculiar applications of the word “trans,” we’re going to use another adjective like “short” or “white” in comparison. I like to call this the “grammar ghetto.”
Shiv is a transgendered woman.
Shiv is a shortened woman.
Shiv is a whitened woman.
As far as I know, there is no English dialect where adjectives are turned into verbs in this manner. I’m reasonably confident that regardless of which specific dialect you learned, “transgendered” is just as wrong in all of them as “shortened” when describing a person.
Shiv is a transwoman.
Shiv is a shortwoman.
Shiv is a whitewoman.
Once again, adjectives are typically separate from the noun they are modifying. I am not aware of any English dialect where they are merged. Trans women are women who happen to be trans, not something else entirely, as might be suggested by mashing the words together. “Short” and “white” are descriptors, they do not replace my womanhood any more than trans does. “I am a short, white, trans woman.”
Shiv and Jane are transgenders.
Shiv and Jane are shorts.
Shiv and Jane are whites.
I’ll give the tiniest amount of wiggle room for this. There are certain contexts where minorities will self-identify in this manner, but it’s typically understood to be dehumanizing when done by majority demographic members. “Short people,” “white people,” “trans people.” Specific to the trans community, the gender-neutral “folk” is typically given a free pass, i.e. “trans folk” or “cis folk.”
Remember that all the rules that typically apply to adjectives in your dialect necessarily apply to the word “trans,” as it too is an adjective.
There is also the kind of cute nickname “enby” (i.e. “NB”) for non-binary people, but I am cautious to use it on a non-binary person without their permission. Others will avoid associations with the binary through the use of terms like “genderqueer/fluid.” In general I don’t see those terms falling prey to the same bizarre grammar ghetto that the word “trans” is treated to–although that may just be that cis folk don’t report on NB/GNC people often.
Go forth and be less awkward in your speech and writing.