The words eccentric and staid are almost opposites here.
"Staid" means something like unadventurous, dependable, and respectable. A staid person would act in a way that wouldn't get too much attention.
An eccentric person on the other hand usually does his or her own things, without caring what other people think or what the normal way to act is.
In the days of the woman's suffrage movement, it was very important that men and women acted a certain way. Women were supposed to be meek, work at home, and be loyal to their husbands. They were taught from a young age to respect society's rules. So, an eccentric person sometimes wouldn't get along with them.