The OPs question was
“I even know of people who won’t even send their kids to Stern or Touro. Why?!! They think it’s not where a religious person belongs.”
Sam2 you’ve just answered her question.
Many Bais Yaakov girl’s will not put themselves in an environment where there is socializing between boys and girls (men and women) whatsover. Not just not to participate, but to be in such an environment. This is the derech they believe to be correct following their rabbonim and mechanchos.
They will be very selective in choosing a work environment as well. Many will only consider a job in a girls school or in an office where the interactions between men and women are distant and formal. They would most definitely not work in a place where there are any single, frum young men.