It's sad, isn't it? The art of chivalry was almost a poetic endeavour with the finest of motives, long, long ago. Knights rode out vowing to treat people fairly, honourably, and to honour God. However, I think you are talking more down to earth stuff, like holding a door open for a woman and this being rebuffed. Some women are touchy and don't want to be patronised, as they interpret it, because they need to assert their equality.
Others feel equal anyway and find it a politeness to have a door opened for them. Many open the door for others. Don't be depressed about it. You are too late to be a knight, but don't lose your common politeness. One woman may rebuff you, but the world turns around more smoothly when people are polite and thoughtful to each other.