There have been LGBTQ characters in DC comics for decades, from heroes to villains to everything in between. While movies based on DC properties have yet to reflect this fact, there has been LGBTQ representation in DC television shows, both live-action and animated.
Within the Arrow-verse, Batwoman, Legends of Tomorrow, Supergirl, and Black Lightning all have LGBTQ characters in the main cast, while The Flash and Arrow have both had LGBTQ recurring characters. Outside that universe, other shows based on DC properties have featured LGBTQ characters, often in lead roles, as seen on Doom Patrol, Lucifer, Watchmen, and Titans. This trend will continue with both the upcoming Neil Gaiman adaptation of Sandman and the HBO Max Green Lantern series.
The DC movie universe needs to catch up, and there are so many characters that could be used to do so. This list will not include any characters that had major roles in any existing live-action adaptations or animated series--although it would be great to see portrayals of Harley Quinn's, Poison Ivy's, or Aqualad's non-straight sexualities outside of cartoons. This is only a few of several interesting and not-yet explored characters in the DC universe.
Apollo
Apollo is one of the earliest gay superheroes in print. Modeled similarly to Superman, Apollo has the ability to absorb sunlight and convert it into energy he can use. He possesses, with this energy, superhuman strength, flight, near invulnerability, and the power to shoot beams of energy from his eyes or hands.
Part of DC's Wildstorm universe, Apollo is part of a secret black-ops team under the organization Stormwatch, which was formed as a planetary defence force against alien attack. Later, Apollo is recruited by superhero team "the Authority," which is willing to use extreme methods and do whatever it takes to get the job done. Apollo is in a relationship with and later married to Midnighter, one of the other heroes in both Stormwatch and the Authority.
Midnighter
The alias of Lucas Trent, Midnighter, as stated above, is married to fellow hero Apollo and was also recruited by the Authority after parting with Stormwatch. Midnighter was bioengineered upon joining Stormwatch, gaining superhuman strength, speed, reflexes, and resilience. He is given a superhuman healing power, making him extremely difficult to kill, and can suppress his pain.
Midnighter also possesses a mental combat computer, meaning he can predict the unfolding of a battle before it starts. While usually separate, the Wildstorm universe merged with the main DC universe in the New 52 comics after Flashpoint, including Midnighter and Apollo. Knowing this, Midnighter and Apollo could be introduced to the DCEU post The Flash feature film.
Sarah Rainmaker
Rainmaker is another member of the Wildstorm universe that Midnighter and Apollo belong to, although as a member of another superhero team. Apache born, Rainmaker's powers manifest when she is growing up on the San Carlos Reservation in Arizona. She can control air and water, creating storms, invoking rain, calling lightning, and creating tidal waves, among other skills. She also becomes proficient in martial arts.
Rainmaker ends up joining Gen 13, a team of genetically altered superhero teenagers. Depending on the continuity, Rainmaker has been portrayed either as bisexual or as a lesbian. Rainmaker only appeared very briefly in a 2000 animated Gen 13 film, so it would be great to see her portrayed in a live-action adaptation, with her attraction to women intact.
Dr. Victoria October
The only non-superhero on this list, Victoria October is a transgender woman who was recently introduced in the comics as an ally to Batman. She is the planet's foremost expert in post-human bio-weaponry and is capable of performing surgery on bio-engineered humans. She has known Batman for many years and helps him in crises where her expertise is needed, most notably, in the "Monster-town" storyline where humans are turned into monstrous beings against their will.
Victoria is notable for not only being a transgender character, but for talking about transgender issues. She discusses transitioning, choosing her new name, deadnaming, and the power of pronouns. With The Batman starring Robert Pattinson set to start a new Batman movie series, Victoria would be an excellent addition to a future film.
Catman
Thomas Reese Blake, otherwise known as Catman, was introduced as one of the more camp antagonists to Batman in the comics. He is an Olympic level athlete who is highly skilled at hand to hand combat and an amazing hunter and tracker. He wears razor tipped gauntlets and carries a "Catarang," similar to Batman's Batarang, as well as a utility belt. Catman has gone through quite a journey in the comics, from a campy villain, to a disgraced joke who other villains scoff at, to picking himself up and transforming himself into a powerful fighter again, and eventually turning into an anti-hero.
In the most recent relaunch of the character, Catman was revealed to be bisexual. Writer Gail Simone had confirmed that he was bi after the end of his previous run, but she didn't have the chance to write it into the story. That was amended when she got the chance to write him again. Catman is another character who could easily be worked into a future Batman feature film.