I don't know if hundred years ago, but thousands probably. In ancient times there were cultures that didn't persecute trans people. Quite the opposite. Having both, male and female characteristics, being ambiguous, was a trait of the gods, like in hindu deities or most creator gods. That's why "trans" people were considered to be closer to divinity than most cis people. They were respected and powerful, high ranking spiritual positions were reserved for trans only. The Sumerian were know for having trans high priests and priestess. Also in ancient north american cultures, two-spirits were usually chamans and spiritual leaders.
Asia wouldn't have been a bad place for trans either. Traditionally, Japanese women used their kimono's belt to flatten the chest and straighten the curves, giving a more male silhouette. The male beauty standard was in contrast, feminine. It was a common thing, specially among young men and nobles, to feminize their appearance and adopt female beauty habits like makeup. Also, there were a few, not many, but a few, people that adopted the opposite gender's dress codes. They weren't discriminated nor hanged. The only trouble were the extremely rigid gender roles. Uesugi Kenshin, one of Japan's most famous daimyou, is believed to have been a woman.
"Transition" would be partially possible. You'd have to take spearmint extract for example instead of synthetic hormones, but I dare to say that natural variations prepared in ancient times would have been as effective as modern HRT, or even more.
In ancient times some of us could have been powerful spiritual leaders, instead we are normal people fighting for basic human rights. Modernity sucks...