The answer is that it both is and it isn't, paradoxical as that is. We do have to realize, that the chivalric tradition (from which modern "gentelmenly'" behavior descends) was created in an extremely sexist society. Because it treats people of one gender different from people of another gender, it is sexist. That said, however, as a general rule it is not a bad thing. My observation has been that most women appreciate it.
However, I think it gets taken too far at times too. I'm not saying that a guy should make his girl pay for dinner, but if she wants to pay for dinner sometimes, he shouldn't say "no, girls can't pay for dinner... that's so silly." To suggest that a woman can't buy dinner for a man is derogatory, it suggests that there is some special status of dinner paying which the woman is not allowed to participate in. And I think we have to realize that women can be tough too. Again, I'm not suggesting that anyone run around haphazardly hitting women, or ever hit a woman for that matter, what I am saying however is that women don't have to be treated like delicate little flowers. Just like men shouldn't be hitting women, women also shouldn't be hitting men. We get so caught up in this idea of "the man always protects the woman" that sometimes we let ourselves miss out on things. I have a friend who absolutely hates the Alien Quadrilogy, not because of any flaw he finds with the films, but because, as he puts it, he "doesn't like watching a woman get slapped around," and as a result, he can't bring himself to watch Sigorney Weaver fight the aliens, because on some level of his mind he believes that a man should be protecting her. As I said once already, women can be really tough, and we have to give them credit for it, part of what I love about the Alien Quadrilogy is that it presents us with such a strong woman, and by that I mean that if I got in a fight with Ellen Ripley, she'd kick my ass. Women can be tough too, and when guys take the chivalric crap too far they can't see this, and that is definately sexist.