I would mos def say im am however:
it depends somewhat on:
what is meant by chivalry OR better yet what do you consider to be chivalrous. In particular, whether or not an individual is including different treatment based on the superficial feature of sex under that umbrella.
what it means for an ideology to be "rooted" in something. In other words, do we regard "rooted" as a crux and essential component of the ideology, or merely descriptive of something's possible origins?
what would be define as sexism. Particularly, whether or not respectful or good treatment of an individual is based on the superficial feature of sex should be considered sexist.