The feminist woman does not deserve to have her door opened for her. In fact, they claim to hate it when a man opens the door for them.
Don't be a chump. Open the door and demand that your woman act like a lady in return.
The reason is that this is when you observe her. A good woman will allow you to open the door for her and she won't get in the way. She will stand on the correct side of the door and if it is a double door she will wait patently for you to open both. In other words a lady knows how to be a lady.
I do recall a few women I've dated walking ahead of me or not allowing me to open the door for them. I personally consider this to be disrespectful. When this happens I often make a sly comment like, "You don't know how to be a lady, do you? Here, let me teach you how to be a lady". I'll then proceed to instruct her how on how to identify what side of the door she should stand on and wait for the man to open it for her. This can be done in a very funny way and you can make the girl laugh quite a bit too.
I now have a girl that does this every time - she shows some f**king respect.