I think it's only sexist if you interpret it as such. People's jaded views on gender roles usually means they're a cynic. Yeah, guys who do this excessively probably do want to get laid. But that's still a stereotype.
Even granting for the sake of the argument that chivalry isn't inherently sexist, how are we to know when someone is being "chivalrous" and when they're not? I think it would be naive to assume someone was being chivalrous and not consider the possibility that they've got ulterior motives.