For the claim that being trans is a fad or something new or whatever, I think one of the best sources to debunk this is the poems of Sumerian high priestess Enheduanna, who lived around ~2300 BCE in the Akkadian Empire. She was the daughter of the world's first emperor, Sargon the Great of Akkad and appointed High Priestess. She is the first non-anonymous author in the entire historical record. Her poems explicitly mention and describe people who transition between genders and occupy genders that are neither male nor female, and also take up roles inside the cult of Inana (or Inanna) [Sumerian] / Ishtar [Akkadian], goddess of sexuality, love, war, and political power, and divine androgyne. In addition, she is even given the power of transitioning someone's gender in what was called the Head Overturning Rite. The poems were so influential they exalted Inanna above all the other gods and they were taught in scribal schools for around a millenia after her death, which is the reason we still have them, because we dug up the course work of scribes who lived thousands of years ago. These quotes come from Inanna, Lady of Largest Heart: Poems of the Sumerian High Priestess Enheduanna by Betty De Shong Meador, which is available on Anna's Archive.

In the myth of Inanna’s Descent to the Underworld, the god of wisdom and sweet waters, Enki, creates from the dirt under his fingernails two ‘sexless’ creatures to rescue Inanna, the galaturra and the kurgarra.

The galaturra and kurgarra eventually became temple personel in other texts. From the poem Inanna and Ebih,

summon a kurgarra for holy office / bestow the sacred implements / hallowed mace and dagger / summon a gala, singer of lamentation / dispense the tools of office / kettle drum and hand drum / summon holy attendants / for ritual head-overturning / priest to become woman / priestess to become man”

The pili-pili and the kurgarra are effectively described as transitioning from one gender to another, via Inanna. From the poem Lady of Largest Heart,

Inanna / dressing a maiden / embraces with full heart / the young girl's handsome bearing

the maid a woman evilly spurned / taunted to her face / sways beneath the wrath / thrown on her everywhere / her only path a wanderer / in dim and lonely streets / her only rest a narrow spot / in the jostling market place / where from a nearby window / a mother holds a child / and stares

this dreadful state / the Lady would undo / take this scourge / from her burdened flesh

over the maiden's head / she makes a sign of prayer / hands then folded at her nose / she declares her manly-woman

in sacred rite / she takes the broach / which pins a woman’s robe / breaks the needle, silver thin / consecrates the maidens heart as male / gives her a mace / for this one dear to her / she shifts a god’s curse / a blight reversed / out of nothing shapes / what has never been / her sharp wit / splits the door / where cleverness resides / and there reveals / what lives inside

the unafraid / who shun her outstretched net / will slip and snag in its fine-eye mesh

a man / one who spurned her / she call by name / makes him join / woman / breaks his mace / gives to him the broach / which pins a woman's robe

these two SHE changed / renamed / reed-marsh woman reed-marsh man / ordained sacred attendants / of ectasy and trance / the head-overturned pili-pili / the chief hero kurgarra / enter estatic trance

Later on in the poem as Enheduanna is listing the powers, or me (pronounced 'may'), of Inanna, she very explicitly states,

to turn man into woman / woman into man / are yours Inanna

I'm obviously biased, but I feel like someone would have to do some pretty intense mental gymnastics to read all this and deny that the segment of humanity that today we in the West call "transgender" did not exist at least this far back and weren't the people Enheduanna is mentioning. Though our contemporay terms don't really work within this context, the kurgarra and gala could be very broadly described as transfem, and the pili-pili could be very broadly described as transmasc. The gala would sing in a dialect of Sumerian meant to render speech of female gods, and some also adopted feminine names.

There's dozens upon dozens of other instances of gender diversity across history and cultures if you go looking for it. Indigenous American cultures have a ton of different expressions of this, today broadly collected under the term two-spirit. In ancient Rome and Anatolia, there were the Galli priests of Cybele. Those are just the ones I know off the top of my head, but there's an almost endless rabbit hole of examples, plus untold numbers that don't survive in the historical record.