Prior to 1989, the Comics Code Authority banned any mention of homosexuality under the umbrella of "sexual abnormality" in comics published in the United States. Since then, comic books have slowly gained LGBT representation, usually with occasional side characters. Queer comic book characters were pretty much always in the periphery until the 2000s, never acting as a major protagonist and certainly not featured in a major title.
In contemporary comics, there is much more representation. While not perfect, there are tons of comic series with progressive, gay characters waiting to be discovered by the masses. The time of delineation between gay comics or queer comics and more "traditional" fare is coming to an end. If you need proof, just check out these amazing comic book characters!
Since Harley's solo title launch in 2011, and her pop culture takeover thanks to Suicide Squad's success (flaws aside), she's become one of the most identifiable characters in the DC Universe. This is mostly a good thing.
Unfortunately, she's still often recognized as "The Joker's Girlfriend," which takes away from any name she's built up for herself. That's not even mentioning that the Joker is a physically and emotionally abusive partner, and nobody should ever be with him. Harley's relationship with Poison Ivy, by comparison, is significantly healthier and, frankly, adorable.
Batwoman was one of the first, and remains to be among the few, queer comic book characters that headlines her own title published by DC. Kate Kane, dishonorably discharged from the military while Don't Ask, Don't Tell was still in effect, finds herself inspired by Batman to take up the vigilante mantle herself after an encounter with some unsavory people. Greg Rucka's Elegy is a gorgeous origin story for her character and definitely a title worth checking out.
Hulkling (Teddy Altman if you're into secret identities), is a shapeshifting Skrull prince who was taken to Earth for his own protection during the Kree-Skrull war. On Earth, he was raised by a single mother. Apart from that, we don't learn much about Teddy's youth in the pages of Young Avengers, where he's graced the team with his presence since its formation back in 2005. On the team, Teddy meets Wiccan (Billy Kaplan) and starts one of the best romances in comics.
Mystique is an interesting being to say the least. She's a mutant with the ability to look like anyone she could possibly imagine, and yet she chooses to identify as a biological female who is attracted to both men and women. This is an entirely unique character trait that hasn't been explored in other titles.
Having the ability to literally conform your body to whatever you desire is overwhelming enough. But once you add on the social pressures of conforming to the "sexual norm," and deciding to actively go the other way? Mystique's strength is off the charts at that point.