Where are these 50Hz noises from?
As others have said, the 50Hz is almost certainly mains-related.  You say the target has a differential receiver, but you don't say if the "main circuit", which is receiving the feedback signal from the target, uses a differential receiver, or what the signalling levels of the feedback signal are.  Even assuming a differential circuit, any real differential receiver has a limited common-mode range, which you could easily be exceeding.  Connecting your system ground to earth ground likely reduces the common-mode 50Hz noise to a level that your receiver can tolerate.

Switching power supplies such as the one you show generally will have a capacitor bridging across the gap between the primary (mains) and secondary (output) side (commonly referred to as a "Y" cap).  Its function is to reduce interference generated by the power supply switching circuits.  Because of this capacitor, and the parasitic capacitance between the primary and secondary of the transformer itself, the output of the power supply can have a very large (>100V) AC voltage with respect to earth ground superimposed on it.  This AC signal has a relatively high source impedance, because the capacitor is relatively small, and thus has a high reactance at the mains frequency.  Because of this high impedance, it is not a safety hazard (unless the capacitor shorts, which is why specially rated capacitors are used for this function), but if you have a high impedance signalling circuit, this can overwhelm it.

When you test in your lab, if both the main circuit and the target are floating with respect to earth ground, then everything is riding this AC component together, and there is no problem.  When you take it to the real world, if the target device has a connection to earth ground (even a small capacitive connection), now you have a large potential difference between the main circuit and the target, and the problem occurs.  By also connecting your main circuit to earth ground, you greatly reduce the potential difference between the main circuit and the target, so your receiver is able to function.

You also don't give much information about the distance between the main circuit and the target device, the type of cabling used, and so on.  The more information you provide, the better the answer you're likely to get.