I still haven't managed to find a love triangle in which are three members are not all hetero. As in, the *two people vying for the attention of one person are of the opposite gender. *

I think Atashi wa Bambi & Bara no Tameni were some of my first works that featured this at all. The most recent work I've read w this trope was Ichinose Kyoudai wa Gaman Dekinai. I'd like a more obvious triangle/square/polygon/whatever, though. One where the lgbt pairing has a fighting chance.

Ex:
Het or bi male & lesbian or bi female going for a bi female.
Het or bi female & gay or bi male going for a bi male.

Something like a true triangle where A is in love with B who is in love with C who is in love with A is good too, if at least two characters of the three are bi or gay.

Also, to make this even harder, I'm looking for a manga that isn't yaoi/yuri, and doesn't otherwise objectify or fetishize lgbt characters/relationships. If it is yaoi or yuri, pls only recommend it if it's not oversexualized &...well, fetish-y.

90s child waiting for last chapters of Glass Mask to be scanlated.

If you don't mind anime, there's HaruChika, with the male and female MC's fighting over their (male) teacher. But, as opposed to them both having a chance, imo neither of them do, as the teacher is fond of them but is a decent adult and will definitely turn them both down. It's a lovely story that's totally disliked by anime fans for some reason. Based on an ongoing LN series, which has very slow-paced and irregular updates, unfortunately.

I think Kanojo to Kamera to Kanojo no Kisetsu might fit, but only the first volume has been scanlated so I can't be certain.

I-Ren, sort of, only with a lot of excuses being made along the way and the male love interest being abandoned more than once by the other guy in favour of the girl. But it is shoujo, and so defies BL tropes for the most part.

Cantarella, kind of. Despite the protagonist never having a chance with the other guy, it was treated fairly seriously instead of being passed off as a joke/phase.

Crush on You - The love interest is very oblivious and cutesy with everyone, so I can't tell whether the girl ever had a chance with him or not. But he did seem quite attached to her, to the point that most readers were disappointed when it ended up going the shounen-ai route.

The protagonist in Indigo Blue is a bi woman who seriously considers whether to settle down with another girl or a guy. It is yuri, though.

And, well, definitely Kyuuso wa Cheese no Yume wo Miru and its sequel, but they're yaoi and feature quite a lot of sex. However, the serialisation was in a josei magazine, not a BL one. Definitely one of the better yaoi out there, but idk whether you'll like it.

That Summer (KIM Hyun) might fit, but I dropped it fairly early on, so not certain.

Nanashi no Asterism, maybe. I haven't read it yet so this may only be my faulty impression.

Girl x Girl x Boy - Female lead likes her best friend. Best friend likes this guy. The guy likes the female lead.

Basically you go to find out that the best friend is actually in love with the female lead, but is afraid of the societal issues of a same sex couple so she tries to drive the female lead away by claiming to like the guy. The guy is a real champ in this story because once he finds out they love each other, he does his best to help them get together and to support them.

I'd like to see a triangle where it's the point if view of the male lead trying to get with a bisexual girl and his love rival is a lesbian. I've seen many where it's from the point of the lesbian, but sometimes it doesn't end well for her.

Edit: calstine suggested Kanojo to Kamera to Kanojo no Kisetsu and I've seen the raws.

It's like Girl x Girl x Boy. Female lead is in love with camera girl. Camera girl is in love with her guy childhood friend. The childhood friend is in love with the female lead. Difference is the camera girl is actually in love with the guy. Camera girl gets close to the female lead all while trying to get with the guy. Camera girl even gets to the point where she tries to have sex with him. He rejects her and the female lead consoles her. Eventually the female lead and camera girl have sex, but then camera girl disappears. The guy and female lead stay friends and years later he tells the female lead that he's found camera girl. The female lead goes to meet her and it ends with them embracing signifying that camera girl loves the female lead now.

I know it's been a long time since you posted this but in case you still care, That Summer (KIM Hyun) fits exactly into your description. It's a love triangle between a straight girl, a bi guy and a gay guy (well the 3rd guy could be bi I guess, it's been a while since I last read it but I doubt it). The 2 guys used to be in a relationship and it's mainly from the POV of the straight girl who befriends them (kinda) and somehow keeps getting involved with them.

It's very difficult to tell who the bi guy is going to end up with. The characterization was great as well from what I remember.