She was also criticised for not having the same religious background as Kane, who grew up Jewish, according to The Washington Post.
Rose deleted her Twitter account after the campaign and trolling, tweeting emotionally of her disappointment at the abuse she had endured.
"Where on Earth did 'Ruby is not a lesbian therefore she can't be Batwoman' come from — has to be the funniest most ridiculous thing I've ever read," she tweeted.
"I came out at 12? And have for the past 5 years had to deal with 'she's too gay' how do y'all flip it like that?
"I didn't change. I wish we would all support each other and our journeys."
Ahead of the show's premiere, and several months after the Twitter campaign, Rose told Glamour magazine she didn't expect to attract such controversy.
"I didn't think people would care so much that I was cast," she said.
"But on my deathbed, I'm not going to be like, 'I really wish that more people, more strangers on the internet that I didn't know, liked me'.
"Some people will love the show, some people might be surprised and find that they really enjoy it, and some people might not see themselves on the screen and therefore not see the point. But there's obviously plenty of shows for people like that. There's plenty of shows for white old men."
The show, which was commissioned by the CW network in the US, is set three years after Batman mysteriously disappeared from Gotham.
Kate's father, Jacob, sends her away to military school after her mother and sister are killed.
She returns to Gotham in the first episode as the dangerous Alice in Wonderland gang is targeting Jacob and his company, the military-grade Crows Private Security.
Batwoman premieres 7pm October 7 on TVNZ On Demand, the same day as the US.
