Rather than the Mulan comparisons they really should've just billed this as "Japanese-inspired retelling of Robin Hood"

[Renoir]

Considering that making Mulan references just because the heroine dressed up as a man has an unfortunate Orientalistic/"all Asians are the same" tone to it, it's better to just compare it to something else. The more I think about it, the more that I see the Robin Hood similarities.

Maid Marian/Marion dressing up as a boy and then running off to join the Merry Men is something that did happen one of the many versions of the Robin Hood legends. One of the really old one, in fact, around 1700s I think. Not only did she dress up as a boy, she actually managed to beat Robin in a fight too.

The princes and the messy imperial court can be Prince John and the Sheriff and Sir Guy equivalents. It's also a thing in various incarnations of the Robin Hood legends that Maid Marian is being pursued romantically by the antagonist characters, and that she doesn't like any of them.

Some versions portray the Merry Men as indeed a rebel group aiming to get rid of Prince John, although I believe some versions had a convenient ending where King Richard returns and suddenly everything is fine.

The similarities are rather superficial, but to me it sounds a bit closer/more relevant than making comments about Mulan. I mean, maybe Renee Ahdieh herself didn't realize it while writing, so it didn't really occur to her that it's a rather apt comparison.