I always have done, I also offer people my seat on public transport. I will not be happy if people start doing the same for me on a regular basis though
I was always brought up to always hold the door open for others and to also thank those who held the door open for me. Now when I am out and about and I see someone behind me walking towards a door I am going through, I will always hold the door open or thank them when they hold it open for me without a second thought.
Well, there is nothing wrong in trying to hold the door for someone that is coming right behind you. That is a good way to ensure that others see you as being courteous and respectful and it is important in today's world.