Time to pull the plug
"Contrary to an earlier posts on the subject, the shielding process appears to involve deleting the data,rather than denial of access to it"
Wrong. In some cases (ie adopted children) you have to keep re-applying to have your child's details shielded. I doubt that the data is deleted every time and then re-populated. If it was easy to repopulate the data the system wouldn't need to exist in the first place.
Of course the rules and working practices vary across the country. There is no consistency. Every council makes up their own rules.
"ContactPoint does not hold much personal data"
Really? Personal data is personal data. Just because you might not consider it "much" doesn't make it any the less valuable.
You also can't check that the data held about you is actually correct.
Regardless of the security applied it still isn't going to stop someone with access abusing the information. This already happens with other IT systems, the difference with ContactPoint is that it places lots of eggs in one basket and potentially threatens the most vulnerable.
The whole system is a disaster waiting to happen and should be binned immediately.