Is there a single word other than manipulator for a woman who uses her sexuality to get a man to crush on her and then act as her champion for idiosyncratic reasons that have no basis in fact?
The word I would use is seductress:
A woman who seduces someone, especially one who entices a man into sexual activity.
Surprisingly enough, Urban Dictionary's top definition for the word doesn't involve sex, but instead defines the word in a bit more nuanced way:
Beautiful girl who has power and control over another person.
Consider a femme fatale TFD
an alluring or seductive woman, esp one who causes men to love her to their own distress
Inspired by “The Postman Always Rings Twice,” a superb psychological-suspense tale starring an enigmatic femme fatale. Washington Post May 21, 2018
or a siren, from Greek mythology vocabulary.com
a woman who is considered to be dangerously seductive