I always found the concept of a man opening a car door for a woman exceptionally insulting to women. I'll open doors for people when I'm walking with them, man or woman, but running ahead of a woman to open the car door for them is cringeworthy * 10. I get second-hand embarrassment shivers just thinking about doing it on a first date.
I like strong, independent, and capable women who are perfectly able to open car doors for themselves. Women who can hold their own in a conversation, are comfortable splitting a check, who are smart and educated, and who don't need to me protect them like they are delicate flowers. I have never been with or talked with a woman in my social group (that I know of) who expected a man to open a car door for them.