Schrodinger's Heroes -- Science fiction about quantum mechanics and saving the world. Diverse sex/gender/orientation of characters. Mix of romantic, erotic, and nonsexual content. Quinn is typically some flavor of genderqueer, transgender, nonbinary, etc.
Torn World -- Science fantasy shared world about temporal technology gone horribly wrong. Wide diversity of characters. Mix of romantic, erotic, and nonsexual content. Worth noting is that Northerners are considered nonmonogamous unless otherwise specified; serial monogamy is the norm for women, while men are not required to stick to one partner per month unless they wish. Character sheets: Omorth (asexual), Tekura (homosexual, also monogamous which is queer in his culture), Vlaran (lesbian).
The Adventures of Aldornia and Zenobia (on Serial Poetry page) -- High fantasy about happy, sane, living lesbians.
The Arc of Joan (on Serial Poetry page) -- Steampunk with Jeanne d'Arc as genderqueer.
An Army of One: The Autistic Secession in Space -- Sociological science fiction with lots of characters who are asexual, aromantic, or celibate.
Clay of Life -- Jewish historic fantasy about golems and their friends. Being constructs, the golems are asexual. Yossele the golem and Menachem the blacksmith are firmly attached to each other, however, in what might qualify as a queerplatonic relationship. It's not romantic but they are living together.
Fiorenza the Wisewoman -- Italian historic fantasy with a minor but repeating subthread of challenging gender roles. Notably Fiorenza sometimes wears trousers, and Giacinto customarily wears skirts. These two are heterosexual and falling in love with each other.
Fledgling Grace -- Contemporary spiritual fantasy with assorted examples. The priest is celibate. An incubus and a succubus change from sexual to asexual after contact with human aces. The goldfinch is genderqueer, who binds her breasts and wears a t-shirt that says "Boi." There are mentions of homosexual and transsexual people in various places too.
Frankenstein's Family -- Gothic fluff about two scientists, their son, and their village. Victor Frankeinstein is transgender and has a queerplatonic relationship with Igor. There is a lesbian couple in the village too.
Hart's Farm -- Historic Swedish fantasy, and the one-stop-shop for QUILTBAG everything. Mix of romantic, erotic, and nonsexual content.
Kung Fu Robots -- Science fiction wu xia with androids who are mostly asexual, neuter, and neutrois. A few of them have selected a polarized gender.
Monster House -- Suburban fantasy about a family with mixed human and nonhuman characters. Some of the monsters have family ties but others probably don't reproduce sexually. "Unspoken Noise" introduces a gay nephew.
The Odd Trio (on Serial Poetry page) -- Fantasy about a polyfamily of three members, two of whom are transaffectionate heterosexual and one of whom is asexual.
The Origami Mage -- Asian fantasy about two rival paper mages. While their sexuality is never made explicit, neither has shown an interest in romance; their primary relationship is their rivalry with each other. So if you count "nemesis" as a flavor of queerplatonic, that's one possibility.
Path of the Paladins -- Spiritual fantasy about paladins trying to restore order to a shattered world. The two female leads are explicitly asexual, as mentioned in "Bouquets of Bygone Days." So are most, but not all, other paladins in this setting.
Poems About Phobic Starships (on Serial Poetry page) -- Variously dark and erotic science fiction about sapient technological beings who can shift shape, and hyperspace aliens. Some of this is body horror; some amounts to transaffectionate kink.
Polychrome Heroics -- Superhero fantasy with lots of characters exploring many flavors of diversity. Damask is a plural person whose headmates include Mira (lesbian), Clarity (neutrois, sapiosexual), Ham (gay), Clement (homoromantic asexual), and Maze (hetero demisexual). Alicia Martins / Dr. Infanta, introduced in "Lifeyears," is essentially asexual due to a body trapped in childhood. Tierra Smith, introduced in "Throwing Souls Like So Much Clay" is lesbian. Calliope and Jayce Olson are transgender.
The Steamsmith -- Steampunk about a black, female, British steampunk engineer; Maryam Smith is genderqueer taking a masculine social role. Among her friends are Aalim and Taysir, a gay couple, also alchemists.
Walking the Beat (on Serial Poetry page) -- Contemporary romance about a lesbian couple living in Jamaica Plain.
Didn't see someone like yourself on this list? Drop by any Poetry Fishbowl or other open prompt call and ask me for what you want.