The most important thing to note here is that we're not actually using "trap" as a transphobic slur at all. The character who's being called a "trap" is being accused of pretending to be a girl on the internet in order to curry favor with her male co-posters. She is NOT being accused of being a transgendered woman -- the idea is one of deception, not trans*.
This is important to note, because the word itself is not ALWAYS used as a slur. In fact, in common internet parlance (especially on 4chan), it's used for exactly the purpose we've used it: to suggest that someone is not actually female, but pretends to be (and is quite convincing about it). Thus, a "trap": someone who fools men into thinking he is a she, trapping them into flirtatious behavior, including money and favors.
This ... is both transphobic and misogynistic. People opposing legal rights for trans people also cast their worries as only targeting "fake trans people" in an attempt to avoid accusations of discrimination. And the whole idea that one pretends to be a woman for favors is the sort of sexist nonsense that, rather than targeting people for their acts of manipulation, decides to make it a matter of gender and women inherently obtaining advantages from men who apparently throw things at random people over the internet. Implicitly with the promise of eventual sexual intercourse, since apparently giving people stuff from outside your sexual orientation is out of the question. Maybe some men, convinced of this same ideology, attempt to use it against others who are absurd enough to send strangers things and then don't accept the responsibility of their actions, but they can be assholes without people conjuring the fear of "fake women" that is also a dangerous meme in society.
This is very naive. Claiming to be a woman in an online communities obviously changes the perception of the person, to differing extents depending on the community in question. It tends to garner negative or unwanted attention along with the positive, but as a general rule it garners attention - which is why people do it regardless of gender or trans status. Attention is inherently valuable online, and a limited resource. People claim to be all sorts of things to bolster their arguments.
Which works out well, actually. Being appropriately skeptical of anything a person claims about themself means you have to examine what they say, undistorted by what they are.
And when what they say is "I'm female! Now pay attention to this..." I don't care whether it's true. I just know that, while their argument may have merit, they're also seeking cheap attention, and that's a bad sign.
Anyway! They're using "trap" to describe this very common practice. Not trans people. The fact that some violent criminals have called their victims traps is irrelevant, as is the fact that some people doubt trans people's status as trans. Those people don't have any right to define the word.