I don't know how anyone else handles this issue in their own lives, but I happen to hold the door open whenever there is someone near me about to walk through said door. I think it's a common courtesy and a nice way to show fellow human beings that we care about them at least a little bit, even if we have no idea who they are. I'm also flattered when people put in the little extra effort to hold a door open for me. However, I am significantly bothered when men go out of their way to open doors for me, whether I know them or not.
I've been told that this is one of the "petty" or "annoying" attributes of my unwavering feminist beliefs, but hear me out. The concept of men holding doors open for women goes back to the idea of medieval "chivalry" or men treating women differently, more kindly perhaps, because they are women. Men have always been expected to take care of the women around them, whether it's their wives, mothers or daughters. Fathers give away their daughters, men are expected to provide a comfortable life for their wives, sons take care of their elderly mothers.
At the root of all of this is the understanding that women cannot handle everyday life on their own. It seems extreme, but in reality, men wouldn't carry bags, hold doors, pay, or a number of other things for other men. There are behaviors that are reserved in our society for men towards women, and holding open doors is one of those behaviors. These expectations come from a place of believing that there is a difference between the two genders. There are differences between the sexes, absolutely, but gender refers to the concept of how people act in society, not their biology.
When we generate different expectations as to how people of varying genders should act, there will always be one that is considered less than. Human beings naturally put things in hierarchal order, so when we see a difference, we evaluate which is superior. The gender difference is one of the most obvious in the human world. The first thing you identify about a person is often their gender or their name, but name often indicates gender. Women are different from men and are quite obviously considered the inferior of the two. So as an extension from this understanding, men take care of women and do the things they are not considered to be capable of.
Things women aren't considered capable of include politics, science, math, making money, physical labor, and loads of other things. In our world, these things are done by predominantly men, and going with the same logic, opening doors can be seen as in the same category. If men see women as needing them to do something as simple as opening a door, how are they ever going to see us as capable of running a corporation or a country? How are we ever going to gain respect in order to earn equal pay?
I know it seems far-fetched and many women have said to me that women deserve small niceties because of the mistreatment the male gender has put them through. However, I see men opening doors for women as an extension of institutional sexism and part of a society that consistently sees us as second-class citizens. I want to live in a world where we all open doors for each other, both literally and figuratively. So open the door for whoever's around you and men, just open doors for women when it makes sense. Don't go out of your way to help a woman by opening a door, and try opening doors for the men around you too.