Interesting.
I’m all for doing nice things for people, but should they be done based on gender? If the underlying ethos of chivalrous acts is that “this person is less or less capable than me because she is female” is that healthy? I don’t think so.
I would be quick to help anyone with a handicap (in wheelchair, blind, etc) or someone who is infirm due to old age or an obvious injury, but is going beyond that—based on gender—good? If I hold the door open for someone I think it should be simply because I got to the door first and holding it is a polite thing to do. I would do this for a man or a woman. Similarly, I might do all the things you mentioned for my other half—even though he is a man—because he is special to me. It’s great that Mike does those things for you because he is a your companion, but do you expect other men should do those things for you as well? If you expect men to do those things for you, but you don’t expect another woman to do them I think that IS sexism.
I’m with tonymctones: I think chivalry does undermine the equality and esteem of women. But special courtesy between lovers is does not because it is something different.
It would be great to hear some lesbian opinions on this. The other day at the gym on the magazine rack I saw and issue of Jane & Jane magazine http://www.janeandjane.net/
I'm not lesbian but bi is close
I feel what Laura's described that Michael does ( and tony ) as being chivalrous , gentlemanly , polite , and a very nice courtesy .
Based on gender ? there's the rub .. yes , if a man just walks into a door in front of me and allows it to close without an offer in my direction .. he's rude .

But if I were a man I wouldn't "expect" that courtesy.
Now since I'm bi and if I'm on a date with a woman , I find that we both do such things for each other , I've opened doors for girls and had chairs pulled out for me , so I can't see any difference there. I think of it being well mannered , and considerate.
For the type of things like taking care of the bills , then ummm no ..if the guy is doing it because he thinks she can't ...he's an ass and Yes a sexist.
The mindset of the person doing the gesture is what makes it a nice thing or a sexist act.
no ?
ps Laura your ideas on what the next President should be is very well said and I agree wholeheartedly ,