There are people who comment on every Hunt: Showdown 1896 news post that the game
would lack LGBTQIA+ representation, mostly to bait people who are against such representation
and to get steam points for it. This (unsurprisingly) works, and stirs up more hatred against queer people. It's also not true, because there is some queer representation in Hunt: Showdown 1896.

Alison Davies and Josie McGowan are the very first mention of a queer couple in the game.

Allison—the woman she would now meet—had sought Jos out, and they had progressed from cautious silence to confessional outpourings, from wary strangers to friends, and then further.

A sentimental Rival 78 with an elegant design. Property of Jos McGowan and a gift from Alison Davis, given after the pair cashed in their first bounty.

Note: The spelling of Alison/Allison is inconsistent.

Sources:

https://huntshowdown.wiki.gg/wiki/Lore/Bad_as_They_Seem
https://huntshowdown.wiki.gg/wiki/Weapons/Rival_78#Alison-0

Circe Elias (The Witch Hunter) and Mary Burgess (Hail Mary) are another queer couple.
They may have broken up, judging how Mary's letter to Circe ends. Doesn't make it less queer.

So you would only be sacrificing your life, and the love we share, at the altar of crude, human vengeance.

I have shared everything with you, shared my heart and stained my body, in the hope I could bring you peace.

Every day brings a new chance to revoke my words and chase everlasting joy with Sister Burgess.

And there you were. In that hidden sanctum was your shoulder, your scent, your hypnotic hands. In many, many moons I have not felt peace with my back turned, but the bumps along my neck have calmed with your presence, your partnership on the Hunt.

Source:

https://huntshowdown.wiki.gg/wiki/Lore/Journal_of_Circe_Elias

Through she preferred the fairer sex, Lulu Bassett got by taking men to her bed. When she learned that she could make a better living taking men to their graves, she decided to put her charms and instincts to use in the Hunt.

Sophia is agender, which was stated by one of the Narrative Designers during a stream for
Trans Day of Visibility in '23 (wich featured non-binary character Viper and Lulu, Sofia's partner).

For every man I've had to deal with, I've met beautiful and powerful women. One has caught my eye. Never stepped foot into the Saloon, just stands outside and watches. I tried speaking to her once but all she did was stare at me like a fox about to eat a rabbit. God, I'd let her. From then on whenever she came, I'd catch her watching me.

I could write a damn sonnet about all the things I want to do with this woman. Anyone who dies to the bullets from her gun are lucky that she's the last thing they see. Even watching her take a swig from a flask by the fire is enough to make my heart race and by hell's fire she knows it. She catches me staring, I can't help it, and the left side of her mouth moves up ever so slightly. If she'd let me, I would kiss that smirk right off her beautiful face.

I joke with her that we're married, we took the vow to join the Hunt together after all, and that she'll never be rid of me. I think she gets the idea of what I'm saying, and she just holds my chin in her fingers and looks at me for a while. It drives me mad. When the hell is she just gonna kiss me? When can I take her to the bed and do more than sleep? I want to see that stoic silent face scream for me. I wish I knew enough of her language to tell her how she makes me feel, I wish I could tell her how much I need her.

Sources:

https://huntshowdown.wiki.gg/wiki/Hunters/Lulu
https://www.youtube.com/watch?v=A0D39_f0Sxg :3
https://www.youtube.com/watch?v=s74PtsNm2Tc&t=365s
https://huntshowdown.wiki.gg/wiki/Lore/The_DeSalle_Shootout
https://huntshowdown.wiki.gg/wiki/Lore/Tide_of_Corruption_Story
https://huntshowdown.wiki.gg/wiki/Lore/Desolation%27s_Wake_Story

A body count nearing the hundreds, yet no inkling of a name, face, or even gender. Westerners call this Persian assassin "Viper," for they’re silent and cunning like the slithering creature, with a poisonous signature move. When they sparked Chary’s interest, their life was bound – or doomed – to change irrevocably.

The Viper is referred to by they/them pronouns, and is stated to be a non-binary character.

Sources:

https://huntshowdown.wiki.gg/wiki/Hunters/The_Viper
https://www.youtube.com/watch?v=s74PtsNm2Tc&t=290s
https://huntshowdown.wiki.gg/wiki/Lore/Serpent_Moon_Story

Thomas Bridge (The Mountain Man) once was in a relationship with another man.

The shotgun of a man Thomas Bridge had called by two names: "Dearest" and "Bastard". This weapon remains the only fitting memory of a nemesis and lover from a life Bridge has long since left.

Source:

https://huntshowdown.wiki.gg/wiki/Weapons/Slate#Eulogy-0