The latest addition to The CW’s pantheon of superheroes is “Batwoman.” She’s tough. She’s smart. She’s a lesbian.

It’s the first time a TV show has been headlined by a gay superhero. Kate Kane is hiding her identity as Batwoman, but she’s out and proud. And this is not a TV invention. The character was reimagined and reintroduced as a lesbian by DC Comics in 2006.

(She’s not TV’s first lesbian superhero, just the first to be the main character. On “Black Lightning,” Anissa Pierce/Thunder — played by Nafessa Williams — is gay.)

The reimagined comic book Kate Kane also was distinctively Jewish.

By the way, Batwoman is not the same character as Batgirl. Kate Kane is Bruce Wayne’s cousin, and, as the series begins (Oct. 6, The CW/Channel 30), it’s been three years since Batman disappeared. So Kate assumes the identity of Batwoman.

She’s not a particularly high-profile DC Comics superhero, but Batwoman has her fans. And when Australian actress Ruby Rose was cast in the role, she quit Twitter because she was trolled and attacked for (a) being wrong for the part, and (b) not being Jewish.

The first part has, unfortunately, become the norm on social media — some comic book fans turn mean and nasty when their expectations aren’t met, even without actually seeing the actor play the part.

(Rose made her first appearance as Batwoman in the “Flash”/”Supergirl”/”Arrow” crossover that aired in December 2018.)

(Photo courtesy of Kimberley French/The CW) Ruby Rose as the title character in “Batwoman.”

In addition, under the #KeepKateJewish hashtag, fans demanded that Kate Kane retain her Jewish identity. And there’s nothing wrong with that. There are a few Jewish superheroes — the Thing, Doc Samson, Green Lantern in some incarnations (but not the 2011 movie) — and none has ever headlined a movie or TV show. Diversity and representation are good things.

But it crossed a line when some demanded the actor playing Batwoman be Jewish, arguing that only a Jewish actor can authentically portray the Jewish experience. Are these fans suggesting that actors must be of the same religion as the characters they play? That they be excluded from playing characters of any other religion?

That would severely limit the opportunities for Jewish actors. I’m thinking the #KeepKateJewish warriors aren’t in favor of that. And yet they’ve gone online to express their “disappointment” and “anger” that Rose isn’t Jewish.

(Chelsea Rothman, who started the #KeepKateJewish hashtag, tweeted that “ideally, a Jewish actress would be great, but what’s more important” is making sure the character Jewish.)

Others are more strident. To extend their objections even further, can only gay actors play gay characters? Should gay actors be precluded from playing straight characters? Can only an actor of Chinese descent play a Chinese-American character? That would be a problem for “Fresh Off the Boat” star Randall Park, whose parents emigrated from Korea.

Actors aren’t the characters they play. They’re not really cops, doctors, serial killers or superheroes. Marion Ross, a Christian best known as the mom on “Happy Days,” was widely acclaimed for her role as the matriarch of a Jewish family on the short-lived “Brooklyn Bridge” (1991-93); Jewish creator/producer Gary David Goldberg (“Family Ties") based the character on his own grandmother.

No, Asian, African American, Hispanic and Native American characters shouldn’t be played by white actors. And if ethnicity isn’t integral to a character, then diversity is the way to go. On “Batwoman,” Kate, her father and the main villain are white; her stepmother and stepsister are Asian American; her love interest is African-American; and the cast includes another African-American actor in a prominent role.

And lest there be any confusion about the title character in “Batwoman,” executive producer Caroline Dries cleared it up quickly at the recent Television Critics Association press tour: “Kate Kane is a Jewish woman.” Rose added: “That answers that.”

If only it were that simple. Yes, Kate Kane is Jewish. But still, there are those wondering if she’ll be Jewish enough.

“We’re trying to find ways of incorporating that without it being a huge thing in the story,” Dries said. "We want it to feel natural,” said executive producer Sarah Schechter.

According to Dries, there was a line in the pilot when “the girls are supposed to be on their way home from their bat mitzvah. And it’s really awkward to shove that into dialogue, and so it ended up getting cut.”

But Kate Kane’s Jewish identity will be part of the character in the same way that the Flash and Green Arrow are, presumably, Christian. It won’t be a big part of the show, because a superhero’s religion doesn’t really come into play when they’re battling supervillains.

It’s certainly worth keeping an eye out to see if Dries, Schechter and the team behind “Batwoman” keep their promise to keep the character Jewish. But if you’re going to obsess over the fact that the actress who plays her isn’t Jewish, just go away.