We already know why Olivia Munn agreed to play Psylocke, but now we know how that character even managed to be in the movie in the first place. Turns out the answer is actually a piece of fan art.
According to writer-producer Simon Kinberg, the original plan for the movie was for the reveal of Apocalypse's final horseman to be a surprise plot twist which was jettisoned. Kinberg told CinemaBlend:
[O]riginally in the script we sort of… I don't know why we made this decision, but we knew that Professor X was abducted in the middle of the movie, and we thought that almost counted as a fourth Horseman. And so that's the way we constructed the original draft of the script. There wasn't going to be a fourth one. The 'surprise' was that Xavier was the fourth Horseman. And then when we were working on the script, Bryan and I at one particular point -- pretty late in the process -- said, 'He's not really a Horseman -- he's not doing anything in the third act of the movie.'
I'm still not sure how adding a new fourth horseman deals with the problem of what Charles is doing in the third act of the movie, but it's nice to see someone decide to remove a twist rather than adding one.
Kinberg said they went through every character which had been a horseman over the years, and decided that Psylocke was the most interesting one on that list. And he had just met with Olivia Munn about Deadpool, which she had rejected. "I said, 'You know, Olivia Munn could be an interesting Psylocke,' so we went on the internet and Googled her images. And one of the first things that popped up was a piece of fan art of Olivia as Psylocke," said Kinberg.
Fan art: it has more influence than you think.