DORORO IS A GIRL.
The above statement is a fact. Dororo is not trans. She is a girl. The term and idea of trans was never a thing historically during the time where this show takes place during the Sengoku Period (1467-1600). Furthermore, the characteristics of this period include many social upheavals, constant warring with opposing warlords, and other forms of conflicts, hence the nickname of "Age of Warring States". As a result, of this hostile, ever changing, and dangerous event, rape and selling their bodies was a very common event for women at the time.
Dororo's parents raised her as a boy because they feared for her safety, especially with Dororo's father's position (most likely some kind of leader). As a result, they raised Dororo as a boy, even though she is a girl. She was not willingly trans, it was due to the idealogies her parents instilled upon her since birth that being a woman was not safe in this era. This is why she feels uncomfortable when people think she is a girl. She views being a girl as sort of a weakness, which is evident in the many horrors she has witnessed on her journey.
Although I do agree there were some (almost zero) people that MAYBE carried some sort of belief that they were trans in ancient times, there is not much historical record to prove this point (there are a few, a FEW I have come across). Your view of "ITS NOT "TO FIT THE CURRENT AGE"", I have to say is wrong in my opinion because the thinking of transgender did not exist.
In addition, people say that she felt uncomfortable when she was exposed as a girl, but I think anyone regardless of gender, would be either afraid or uncomfortable in a situation where he/she is naked in front of a group of people.
Finally, just want to make my point even clearer, Dororo wants to think that she is a boy because it provides her with more security (women are more likely to be attacked or taken advantage of, especially younger ones), and secondly, her parents forced this thinking onto her to protect her.
Another point I just want to bring out, is please stop dragging this gender nonsense into a good anime, it spoils everyone's mood with all this argument. There are not 63 genders, there is only two genders scientifically. Male (XY chromosomes) and female (XX chromosomes), there are other arrangements of sex chromosomes, but these are merely genetic mutations (mostly caused by nondisjunction). Although there are a few people across the world that have these rare mutations, it is not enough, nor is it right to say that they count as genders. THERE ARE ONLY 2 GENDERS.