How about we think about extending helping hands to people in need regardless of stereotypical ideas about who those people are? For a facile (and obvious) example, why hold open doors for all women, when we could wait for a man loaded down with grocery bags and open the door for him?
Chivalry, defined by ancient rules of "etiquette," is formulaic and inflexible. (Did you know etiquette literally means list in French, and once referred to lists of chivalry rules?)
Kindness, on the other hand, is flexible, springing from a place of genuine concern for others rather than from a need to follow rules. Or at least that's one way of looking at it.