Why? It's not like infections only happen in schools. Or that students spend 100% of their time at school. Look at the Disneyland outbreak.
The main reason to require vaccination in public schools is that they're a resource that's supposedly available to everyone. I shouldn't have to expose my kid to other kids who haven't been vaccinated in order to access the public school system. So we require vaccinations there. Private schools are private. That's why you can send your kid to a school that teaches young earth creationism if you want. Likewise, you could elect to send your kid to a school that doesn't require vaccinations. I would support a reporting requirement, though, obligating private schools to publicize in their promotional materials whether they allow un-vaccinated students to enroll. That way parents can make an informed decision.
I think that you are under the impression that it is ONLY transmitted via sex or needles.
Not really. It's transmitted by blood, or bodily fluids containing blood. That can happen without sex or needles but, outside of mother-to-child transmission during delivery, its more rare. I would be much less concerned about sending my kids to a school where some of the students weren't vaccinated against HepB than I would be about sending my kids to a school where some of the students weren't vaccinated against measles, mumps, rubella, pertussis, etc.
Where there's a will, there's a relative.