People DO accept female action stars. It just depends on the movie. Kate Beckinsale did her Underworld shit just fine. Michel Yeoh did a ton of movies in Hong Kong. Uma did it in Kill Bill. Angie did it in Tomb Raider. It's all about the TONE.

Nobody thinks the Indy films are serious. Nobody thinks the female action star movies are serious either. So if you go and make a dead serious movie where a guy falls out if a plane and survives using a boat or a girl kicks a massive dudes ass, yeah, nobody is gonna buy it.