Yeah buddy, they did.
Batwoman already has been a trailblazer for LGBTQ+ representation in comics. After a long hiatus, she was reintroduced to the DC comic universe in 2006 when she was established as a Jewish lesbian, becoming the first-ever lesbian superhero title DC character. Now Batwoman would become the first gay lead character — male or female — of a live-action superhero series. (DC, Berlanti and Warner Bros. Animation previously collaborated on the first animated show with a gay lead, Freedom Fighters: The Ray on CW Seed).
Batwoman would join Arrowverse, which features a number of LGBT characters, including Arrow‘s Curtis Holt, The Flash‘s Captain Singh, Legends‘ Sara Lance and Supergirl‘s Alex Danvers.
Batgirl