I am no comic book geek, but my understanding is that Batwoman has always been a "lipstick lesbian"--which Ms. Rose certainly is not. Hell, Scarlett Johannsen would be perfect for the role.
My comic geek brother is O.K. with Batwoman being gay--because that is what the character has always been. It's when the SJW idiots change the fundamental nature of an established character that my brother goes berserk.
Here's my suggestion to bend everyone's noodle. Let's have someone do an adaptation of the play Othello where Othello is white and all the other characters are black.
Been there.
Done that.
Beam me up.
One movie adaptation of The Fantastic Four made Johnny (The Human Torch) Storm, the full brother of White Susan (The Invisible Woman) Storm, Black.
Batwoman was not always gay, that is more recent I think.
How about a redoing of Porgy and Bess with an all white cast. Mel Gibson as Porgy seems right.