Not sure those points in bold carry any weight.
Women taking opportunities away from men should generally be applauded, in terms of correcting historical imbalance. The converse is obviously a completely different scenario.
Casting a white man as Othello would get you absolutely crucified if it happened today. With good reason. So whatever happened in 1997 isn’t particularly relevant.
Race reverse casting has been used fro Anthony and Cleopatra and in 2014 in Death of a Salesman too:
https://en.wikipedia.org/wiki/Race-reversed_casting
I am not sure that this is not an example of correcting an under-representation of non-binary characters on stage.
For me, every version of a play or story involves some element of re-writing. Casting decisions, directoral interpretations, stage instructions all go towards a unique performance of whatever original material is being presented. I think Richard III and its many adaptations are a good example - Kenneth Branagh, Antony Sher and Ian McKellen play widly divergent versions of the same figure, even if the source material is the same.
Another reason why I personally view the blowback over this decision as out of proportion is that Joan of Arc is already an LGBT icon. The fact we don't know with certainty about her sexuality has led to many people (legitimately in my view) reinterpreting her life and 'filling in the blanks'.
For example, there is a whole wiki site dedicated to her sexuality, cross-dressing and gender identity:
https://en.wikipedia.org/wiki/Cross-dressing,_gender_identity,_and_sexuality_of_Joan_of_Arc
She was subject of a 1931 biography which claimed she was a lesbian:
https://en.wikipedia.org/wiki/Saint_Joan_of_Arc_(Sackville-West)
Articles on whether she was genetically male:
https://glreview.org/article/article-577/
Defended as a queer saint:
http://saints.queerchurch.info/?p=56
Defended as a lesbian:
https://365daysoflesbians.tumblr.com/post/174405676674/may-30-joan-of-arc-1412-1431 (this also shows indivduals and celebrities dressing as Joan did as a performative statement)
And portrayed in a tonne of art as LGBT:
https://qspirit.net/joan-of-arc-cross-dressing-lgbtq/
Joan has even been defended as a trans activist.
This is despite the lack of historical evidence, not because of it.
I am not posting this to convince you or anyone of these views or opinions. I don't agree with them all. But it does show that a historical figure is being interpreted as part of the LGBT community.
Yes, this is a play, and not an article in an academic journal or a piece of art (you may feel that's a key difference, whereas I do not), but I do not see how this has crossed a line, or is providing a radically different interpretation to the story than all the other portrayals above.
Moreover, it is one version of a play. If it is unsuccessful, it won't be run again. But my criticism of the reaction more generally (not yours specifically) is that this is somehow an unreasonable portrayal of a historical figure, when we have had decades of similar portrayals.