Yeah, I think there's a difference between "chauvinistic" and old fashioned gentlemanly, but I haven't seen any evidence of him looking down on them or calling them weak. My smuggler was male though so I only saw how he reacted to female NPCs and companions.
Actually, being and old fashioned gentleman is rooted in traditions of chauvinism. It's important to recognize that chauvinism isn't misogyny. Chauvinism doesn't require a hatred of women. Traditionally defined, chauvinism does require a belief of superiority, but you don't have to have a chauvinist mentality to engage in chauvinist actions and traditions.
Corso believes that women should be treated in a certain way because they are women. That's chauvinist, and nonsense. People should be treated as they desire or deserve based on who they are, what they want, and what they've done. Not their gender.
Opening doors, pulling out chairs, or otherwise "treating a woman like a lady" is rooted in the idea that men should treat women like porcelain dolls or delicate flowers. A man doing these things might not mean anything negative by it, but it carries a negative connotation.
That's not to say that no man should ever treat a woman like a lady, or act in an old fashioned gentlemanly manner. There are no shortage of women who want to be treated that way. But there are also no shortage of women who don't want to be treated that way.
Pulling out a chair for a woman who enjoys that treatment is polite. Insisting on treating all women a certain way because you think that's how one treats women is chauvinistic.