Not really?

The reason we call it "chivalry" (that is, a term based in knighthood and vassalage) rather than "manners" is that it's intended as a relationship of exchange

So, the man does basically protective behavior (taking the outside lane in pedestrian traffic, sparing ladies' delicate ears from shocking language, keeping women from having to stand on the train or open doors, etc) and the women are supposed to defer in some contexts and be equally appreciative in others.

This makes, say, the old timey structure that one should never contradict a lady extremely inappropriate in any context that involves treating those women as equals- work, academia, politics, et cetera. Also there's the assumption of delicacy on the woman's part.

Good manners tends to break down (to me anyway) into a levelling impulse- you treat everyone well with as few concessions to rank or station as possible. (Etiquette is also a means of self-defense, but ymmv there.)