I am not sure chivalry is synonymous with kindness, It could be the knight wanted to gain some benefit etc. Knights were also looked up to by many people. There attributes were bravery, sacrifice, protectors. What better way to exemplify that than to be chivalrous.

To my way of thinking, whether she be dressed up to the Nines or simply in jeans and sneakers a woman deserves to be shown respect and treated with respect UNLESS or UNTIL she has shown herself to be completely UNWORTHY of such.
As an example I cite a recent encounter I personally had, I was walking home from a nearby supermarket after getting a few things I needed when I saw a woman ( in her late 60s - early 70s) at the side of the road with a flat tyre on her car.
I went over asked if I could help her change the tyre, she said to me "Oh, thank you Sir, what a very kind offer, you must be a very true and decent Christian Gentleman.
I simply responded with the truth, "No, Ma'am, I'm an Atheist and was brought up to be a Gentleman who respects others and helps those in need."
She became quite verbally abusive towards me then slapped my face, spat at me before telling me she would rather struggle to change the tyre herself than accept help from a Godless Heathen.
That 'episode' has not changed my attitude towards being 'chivalrous' in any way BUT it has shown me that in some aspects Religion, Xtianity in particular, may have eroded decency in society to some extent.