I think I see what you're aiming at here, and I would say that 1) yes, chivalry can go hand in hand with equal rights. I do believe that treating both genders equally is not the same as making an effort to comport one's self as a gentleman.
I'll give you an example which I think applies to what the OP is suggesting. I work for a security firm, and the client that I work at has both male and female employees. Now if I happen to be around and about the door to the office and not busy with anything, and one of the ladies (regardless of age or appearance) is coming into the office, I will take a few steps out of the way to open and hold the door. I don't necessarily do this for other males, unless of course they're carrying something and need assistance or they happen to be following me in or out of the building. The reason I make an effort to do this brings me to the next point that
2) Chivalry is, for the most part, dead. To me chivalry is, more than holding open doors or pulling out chairs, also about behavior. I'm not at all trying to exaggerate when I say that I think I am the only male at my place of work who make it through the whole day (let alone my whole two years) without making some kind of innuendo, leering, gawking, or other piggish remark about the ladies there.
I may find some of the ladies at my place of work to be attractive, and yes, I most certainly do find the female form to be very beautiful, but I'll be damned if I can't compose myself like a gentlemen and act like it.
So... yeah, I think the concept of chivalry (atleast in my mind) has more to do with your behavior and how you act in general, not just around the opposite sex. You can hold all the doors in the world open for both men and women, but the moment you turn around and disrespectful comment or gesture, then you're no longer being a gentleman, and no longer being chivalrous.
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