I don't think her approach to the upbringing of young girls in an urban setting was that unusual. Most children were taught not to speak to strangers, not to take food from strangers and later, not to take rides with strangers. In actuality, chaperones were usually present when young unmarried women were in public. At the time the story takes place the police did not have the respect and standing they came to have later in the century--they were to be feared as much as strangers and certainly, since most were Irish, maybe even more so.
Probably it made the sisters --Constance at least, more curious about the outside world and the people in it. Why else would she allow the Singer man into her home when she was alone? A total violation of the societal rules of the time. I don't think she would have been any less naïve if she had been less protected.
Interestingly, rather than producing women afraid of their own shadows, it produced strong willful women --most likely from the move to the country where, though isolated, they learned to fend for themselves and become independent when they succeeded on their own. They strode into the world with the self-confidence of survival, though Norma would have been happier going on as usual, without public contact or notoriety.