After the trouble they got into with Street Fighter x Tekken’s win quotes, Ono/Capcom changed stance to say that they don’t have an official stance on Poison. It is a player’s choice as to whether you believe or want to think of her as a biologically born woman, a pre-op transsexual, or a post-op transsexual. Ono admitted this was an attempt to cater to everyone.
While Ono went on to claim this was always Capcom’s stance on Poison, that is not true. Ono himself had stated years before that Poison was transsexual, and the only aspect that was up in the air was whether she was pre- or post-op, as Capcom of Japan and Capcom of America had differing opinions. Indeed, this was Capcom’s stance from even before the release of Final Fight. While Poison and Roxy were designed by their creator to be biologically born women, it was decided by others (and against his design) before the release of the game to recast them as transwomen, due to fears of how American audiences would react towards portrayed violence against women.
On a related note, since Poison got all the fame, people tend to forget that Roxy shared the same status (largely due to forgetting Roxy existed.) Now people mostly just seem to associate Poison as being the trans character.
As for Poison’s general popularity, you have seen the internet, haven’t you? At least seen it in a fashion that hasn’t been heavily censored for your entire life?
EDIT: It may also be worth noting that in the early years, there was plenty of confusion to go around over Poison’s official status, which itself let people believe what they wanted to believe. People blamed Nintendo for forcing the change, even though Nintendo wasn’t involved, and thus didn’t view it as legit. People would say that Poison was only changed to be a guy in the US, even though she was changed for Japan as well. And the like.