Yes, I routinely hold doors for women (actually for anyone who is behind me, male or female), and would give up my seat on a bus to someone (if I rode buses). I have relinquished my seat at the lunch table for one of the lady instructors and have eaten standing up at the cabinets instead when there were too many people in the lunchroom.
If I'm driving, however, I assume the female is perfectly capable of opening her own car door. Most of the time they're out of the car before I am, anyway. It depends on who I'm with and what her level of expectation is. If it's a female of my peer group, I play it by ear. If it's a woman who is significantly older than I, I will offer to push in her chair for her at table, help her with the door, etc.