On a university campus? Probably not well at all.
You would be surprised. Yes a lot of women act that way, but I truly believe that many of them secretly do want the doors opened and chairs pulled out. It's not PC for them to show it, but gender roles aren't completely dead yet imho.
In fact I bet it's a silent majority that still feel that way, they just don't want the scorn of their more vocal peers so they play along to get along. (I have yet to find a girl of any age who isn't thankful to a guy who tightens up her battery cables with a thingamajig or doomajiggy to get her on the road again. :) )