I open the doors for either gender when I Feel I have the capacity to do so. I take pleasure in civility and being a gentleman to others.

If a person is offended by it, I would apologize and state exactly what I stated in the first paragraph. I would then ask them would you prefer for me not too open it for you, or would you prefer me to ask?

I won't be offended, but if the person prejudges my actions based upon another man's without getting to know me or refuses to communicate it to me. It would seem that this person may not be ready to date or should not be dating.

It is also a great red flag moment for me, because I know my intent is pure and good and not sexually or misogynist based, so it reflects on the other person

On the other side it does setup a possibility of a conversation about gender assumptions and relationships needs.