I'm bisexual. I reject the notion that this implies/supports the notion of a gender binary. (Does "bilingual" mean that there are only two languages?)
Many of the people I've dated have been various forms of gender queer. In the spectrum from "stereotypical masc" at 0 to "stereotypical femme" at 100, I stay mostly around the 15-25 range, and since I'm amab, that makes me pretty cis.
I would not say that the gender of my partners "doesn't matter". Gender is often a core part of a person, usually very intimately connected to their image of self, how they move throughout the world, and how our bodies and personalities interact. Of course it's important! But, some of the people I'm attracted to (physically and/or emotionally) are gendered similarly to me, and others have genders that are very different from mine, or much less fixed than mine.
I embrace the term "bisexual" over "queer" because it is more specific. I am "queer", but only because "queer" is an umbrella that covers a lot of things, including bisexuality.
I embrace "bisexual" over "pansexual", because of the fact that the genders of my partners (and other aspects of their body) does matter to my attraction. I certainly have a few "types" that I like, and I think that's fine. (So is not having a type, or being pansexual or omnisexual or asexual or any other thing.)
I also embrace "bisexual" because seriously? fuck the stigma from inside and outside the queer community. Fuck that stigma forever. "Bisexual" is not a dirty word, it is not anti-trans or gender normative, and it is not a dysfunction or a phase.