If you completely isolate the grounding systems you are asking for trouble. You can have a potential difference between the two isolated grounding systems. In the late 80's the company I work for installed a DCS system for a chemical plant. The DCS manufacturer insisted on an isolated grounding system for their equipment. It had 120 volt power so there were two grounding bars in the equipment. One tied to the building electrical system for the 120 volt powered equipment and a second isolated one for the grounding connections to the DCS instrumentation. Complete isolation was maintained and an insulted grounding conductor was installed from the DCS to a grounding electrode system that was about 50' away from any grounding electrode connected to the building electrical system. The next summer they started having problems with board failure in the DCS. The factory rep came out and had us prove that the DCS grounding system was in fact isolated from the building system. We advised that the two systems should be bonded together at a single point, but they said no way. By this time the summer was over and their were no more board failures until the next summer. Same process was repeated. The third summer they finally let us bond the grounding systems together and there were no board failures in the following summers. It appears that even without a close by lightning strike the cloud charges of the effects of remote strikes can create a difference in potential between the two grounding systems. Bonding these systems together eliminates this potential.
Don