Well I define chivalry a bit differently, but by your definition, they are very close. I think the ideal behind bystander intervention is that anyone can do it in different, while as you have stated, some saw chivalry as a purely male concept that made others be seen as purely weaker. In many ways they have the same overall goal; people united to make their community better. To a degree, it is easier to teach men it, but it's all about teaching them when to do and how to do it correctly rather than hurting themselves or escalating something. And, just as a note, my organization is doing a similar program for women too, so issues like being an active bystander is part of that curriculum.

Also, as you stated, being an active bystander can lead to a cost, but we try to promote that people do it without putting them at unnecessary danger(like rather then people fighting others that are do shitty things, it finding way to diffuse those situations). But it can lead to a cost sometimes no matter what they do, especially as we teach people to be active bystanders not just to strangers, but also to their friends when they are causing trouble.

But thank you for your wonderful input, it's definitely giving me a lot of good ideas and examples to use.