I'm in San Antonio (mildly conservative by US standards), and it's rare for anyone to say "ladies first." I can't even recall someone saying it the past five years. People generally hold doors on the merits of the situation (they hold it to keep the door from hitting someone, or for someone who has a hard time moving around).
Violence is not all that common in my circle, so I may have a skewed result, but I think there is a greater tendency to consider more the physical ability of the participants involved rather than focus on the gender, and a lot of discussion actually deals with the "merits" of violence (who did what leading up to the confrontation, their mental states, how offensive/defensive were the participants, etc). Granted, some people will bring attention to the fact that a female is strong relative to other women if she hurts a male who is weaker than her, and some people may still speak with some flavor of the old ways, but the prevailing attitudes are much better than they were historically. It may "help" that much more of serious violence is weapon-related (which can strip away some if not all of a physical advantage) and that men overall do not possess the same physical advantage they did in the past (exercising is more egalitarian today, so social factors do not contribute as much to physical disparity).
But language is a powerful weapon, and while social factors seem to contribute towards women developing it, it's wielded by men as well. There are quite a few people who make a living out of using language as a weapon, and it's generally legal.
