I've never had a woman get mad at me for opening the door for her. I've been told, "No thank you," and maybe I've been smart enough to at least listen, but I've never had a woman get mad for that reason.

Same with offering to hoist carry-on luggage, reach for a grocery item on the top shelf, and offering a woman to walk out of the elevator first. To me this is just polite courtesy as simple and useful as "Hi" and "Thank you."