Please consider the following as food for thought, and not the statements of someone with deep experience in this particular area.
There are two separate safety issues here, parallel paths for the electrical system grounded conductor current, and equipotential bonding for current flow through the earth.
'Objectionable current' of the sort being discussed here occurs when you have multiple connections between the system grounded conductor and 'ground'. This quite simply introduces parallel paths for current to flow.
The NEC addresses this by permitting only a single connection between the system grounded conductor and 'ground'. (Exception for detached structures noted.)
The problem is that the NEC does not control the entire electrical system. Often the electrical system grounded conductor is grounded at the transformer, and then re-grounded at each and every house. Blammo: parallel paths. If each house has its own grounding electrode system, then this parallel path is relatively poor, 10's or 100's of ohms through soil, and very little current flow. But if the houses share a common metallic piping system, then you have a very low impedance parallel path and can see quite a bit of current over the GEC and this 'grounding electrode'.
Breaking the electrical connection to this common metal piping system will substantially reduce the current flowing over this 'parallel path'. There will still be some current, because the pipes are buried in soil, with grounding electrodes nearby, but it will reduce the current to the same magnitude as parallel paths through the soil alone.
However, breaking this electrical connection means that you now have grounding electrodes that are _not_ bonded together. In the even of earth currents, caused for example by _nearby_ lighting strikes or by multiply grounded primary distribution systems, you may see potential difference between these grounding electrodes, or you may see this 'foreign' current flowing on the grounded conductor between the grounding electrodes. The potential between one grounding electrode and another can be quite substantial in the even of a nearby lighting strike. Leaving even a stub of unbonded water pipe inside the home is a risk in the event of a nearby lighting strike. But as I said above, I don't have the experience to evaluate how much of a risk.
I believe that the safe solution would involve either running a four wire service with separate grounded and grounding conductors, treating each service entrance as a subpanel from a feeder (not likely to happen nor be permitted under current rules), or by adding dielectric sections to the water supply pipes _underground_ and away from the house, possibly bringing plastic pipe into the home.
-Jon