Her argument is that since I like both "genders", and I'm in an open marriage, I should be cool with getting with her.

First off, if it someone is "arguing" that you should have sex with them, then you shouldn't have sex with them. This is borderline rapey and predatory as fuck. Second, this person sounds like a creepy stalking narcissist.

Was told I'm just transphobic.

Is this a thing that my other bi sisters and brothers are experiencing?

Yeah. That's pretty much the whole routine they do, and it's why a lot of people (for example, even just the ones here) are pretty bothered by them at this point. It's always "do what I want, think what I think, etc, otherwise you're 'transphobic' and some kind of awful prejudice person." They like to use the awful-prejudice-person tag as a way to attack people for things or get people attacked for things when they don't get what they want for whatever deranged reason they want it. It's just a bullying method.

Bad people have realized others don't like injustice nor bad and wrong doings lately, so they like to use the "I'm the victim" or the "I'm the good guy" act and try to make others out to be the bad people now, so they can manipulate the mindless and gullible to rally behind them in their bad and wrong doings.