R’ Joseph-yasher koach-I admire when people get me to re-think a point. I guess I have an issue with the term chivalry.
CHIVALRY
1: mounted men-at-arms
2archaic a: martial valor b: knightly skill
3: gallant or distinguished gentlemen
4: the system, spirit, or customs of medieval knighthood
5: the qualities of the ideal knight :
To be gentleman like doesn’t mean to be davka like a gentile. If it was considered chivalrous in the goyishe velt for the husband to take out the garbage, then the notion of mentchlichkeit would be out the window?
I think it would be fine for her to open the door to the building if she got there first, but that probably wouldn’t happen because he’s walking in front of her anyway. So, he opens the door, walks in first while holding the door open behind himself and she proceeds. Everyone in still a mentch!
If they reached the drivers side first, I think it would just be strange for her to open the door to the car that he’s driving. That would just be weird. For him to be expected to go to the other side of the car and open it I think would also be strange, and therefore fit in the category of chivalry.
If the lines of mentchlechkeit get blurred and it becomes a concern of chukas hagoyim in other normal mentchlech areas of life, then there is a problem.
(I think tzippi addressed that point wisely and concisely in her post)