See dot.com this is where you are taking it into a subjective approach, there is no right or wrong answer because it is open to interpretation. Some will argue that yes, they are allowed to intermingle if it is for furthering islam, and islam encourages education, thus it is ok for them to mix in schools.

What about a party for eid? They can say yes, although they males and females are not related, we are here to the celebrate an islamic event, so nothing wrong with it.

Let me ask you, is there any mention of there should be people who actively pursue people even in their private dwellings to ensure they are complying?

This is why I hate entering debates based on subjectivity, everyone will go around in circles about what they believe is right and on and on.