Just because it isn't mentioned anywhere doesn't mean it cannot be that way.
No, but it means that assuming otherwise is taking extra steps based on pretty much nothing.
Was the fact that Eirin drank the Hourai Elixir mentioned in any of her profiles? No.
It was mentioned in a IN ending. Miko once being male? Never mentioned anywhere outside Sanae's confusion. And again, she's from the outside, where Shoutoku is considered myth. The bill having his face, as C.Angel said, means nothing; Shoutoku is currently thought as male in the outside world, therefore it's obvious that the bill would have a man's face.
Besides, waving SoPM around as an evidence that Akyuu doesn't mention anything about the matter is just as doubtful. I mean, it's Akyuu...
I shouldn't bother with this "it's Akyuu, she's unreliable!" argument again, but... every single time she's wrong about something, it's glaringly obvious: Eirin and Kaguya are from the moon, Sakuya's past is just a bunch of theories, Mokou isn't the descendant of ninjas, Heaven's true reason for not allowing people in is their own selfshiness, etc. In other words, all the things that she get wrong are things that she has absolutely no way of really knowing (the only people that know the guys from Eientei are lunarians are the playable characters, and I don't think Mokou and Sakuya are too keen on discussing their past, for example). So, unless there's blatant evidence on her being wrong, there is no reason at all to consider her unreliable.
Furthermore, Shoutoku, in Touhou,
is a historical figure, even though she's considered a legend nowadays. Akyuu is a historian. Are you
really saying that she wouldn't even know the gender of that
very famous emperor? Her first incarnation, all but stated to have been Hieda no Are, is from the 7/8th century. Shoutoku lived in the 5/6th century. Unless her gender was already lost merely one century after her "death", there's no way the person that wrote Japan's first historical record wouldn't know it. And since she has her ancestors memories, she'd remember that.
And while I am well aware that the girls like Kasen, Suika and Yuugi are based off on male legendary figures, Prince Shotoku cannot be absolutely dismissed as a figure of legends and not a historical person. The evidence provided is not enough to dismiss a theory completely, just as there isn't enough evidence to support it.
As C.Angel said, Shoutoku IS dismissed as a figure of legends in the Touhou universe. Which is basically what he is in our world as well. Also, bear in mind that, as far as we know, the legends of the outside world are the same as ours, so Ibaraki-douji, Shunten-doji and Hoshiguma-doji are probably thought as male too, which we know for sure isn't the case (unless they also changed genders).
The evidence you have, in-universe, is a bill that supposedly has the face of the dude, and a school textbook. Both from contemporany Japan (the yen note with Shoutoku was printed in 1957), that doesn't even believe Shoutoku existed. Add the fact that there is no good explanation as to why Shoutoku would even
want to change his gender, and I hope you can understand why I find it
very difficult to think of this as a valid theory.
I mean, if you
want to believe that, it's fine. It's not
explicitly contradicted in-universe. All I'm saying is that, at the same time, there is 0 canon evidence to support it at all, so I personally think it's overthinking it to claim that she was once male. It just raises too many questions that don't really need to be raised.