How does Hybrid Ground Works?
The critical reason for the low frequency blocking capacitor is avoiding large DC currents to flow. In any practical application, "ground" is only at zero potential in a very small region; the "ground" potential can vary across a circuit board, equipment chassis, or or larger assembly of equipment (telecom, AC power, building) due to current flow and non-zero resistance. Thus, connecting the shield of the twisted pair to both the sensor and the amplifier could cause such current flow between G1 and G2, since they are different "grounds." Depending on the reasons for the ground loop and the common grounding conductor, it is possible for a little interference to thousands of amps to flow because the two grounds otherwise have a high-impedance connection. This depends on the equipment and other electromagnetic situation at each end of the sensor wire connection.

The use of a capacitor means that high frequency noise/EMI is conducted away from the sensitive in-amp nodes because the capacitor connects the two grounds only at high frequency (where the capacitor presents a low impedance). This also reduces the buildup of large potential on the shield relative to the amplifier due to this high frequency noise because they are conducted, through the capacitor, to the ground of the amplifier.

Further reading:


Ground Design to Control EMI
App note on connecting shielded twisted pairs in different applications