Bat-hypocrite (2019)

Does Batman own the right to being a vigilante as a job? In that case, i think Oliver Queen, Barry Allen, and Kara Zor-El also would get sued here.

No he doesn't own being a vigilante or a costumed superhero.

But Batman does own the Bat-cave - which Batwoman breaks into, the suit - which was altered without his permission and is being worn by the person who stole it (what would you say if someone broke into your room, took your clothes, had a tailor alter them to fit their body then wore them around?), the gadgets - which Batman either made, paid for or invented himself, and the idea of Batman in-universe - which he made based on his own personal experiences and fears. I wonder if Batwoman is also going to go joyriding in the Batmobile or the Batplane...

Look, her breaking into his cave and stealing his stuff is not what i consider okay. Especially since she made her own equipment based on her own personal identity and religious beliefs in the comics which is very empowering. However her taking up the name of Batwoman isn't really stealing who he is. He's still Batman and what the mask means to him is very different than what it means for her.

If she made her own gadgets in the comics, that's what she should've done here. Her taking up the name Batwoman isn't so bad, that's only one point for her versus the several points against her which I listed. They make her religious, yet she has never been portrayed contemplating any conflict between Judaism (which disapproves of homosexuality) and her LGBT lifestyle, and I'm not sure what that has to do with the Batwoman persona.

It's basically a reflection of her identity conflict she has becoming Batwoman. She wants to serve as a soldier, but her only option is to become a vigilante. So the conflict between her Judaism and her LGBT lifestyle is a mirror of that in her civilian life. It's a battle between different parts of her sense of identity that they have used in the comics while in the show, Kate Kane is essentially Batman.

Sounds like there's quite a few layers to the character in the comics. You have a good point about the parallel conflicts of Judaism/LBGT and the solider/vigilante life. Sadly, the TV show seems to just go for some hypocritical, painfully obvious "gurl powah!" SJW angle.

Cause it is easier for a typical CW audience to accept a female LGBT protagonist than they'll accept a Jewish one.

What does CW mean?

The C stands for CBS which partners with them, and the W stands for Warner Bros. which used to own them.