I want to know why the high capacitance of metal oxide varistors
affects sensors, signal sensitivity.
Basically, this question boils down to how would moderate to high capacitance affect signal levels from a sensor. And the simple answer is found in the humble RC low pass filter. It has nothing really to do with MOV varistors - any component that has significant capacitance to ground (or the return wire) can reduce the high frequency spectrum of a sensor output.
A capacitor when placed a cross an AC source will take more current when the AC source frequency is higher. This is because of the fundamental formula for a capacitor is: -
$$I = C\cdot\dfrac{dV}{dt}$$
And clearly, for the same RMS level of signals, higher frequencies have a greater value of dV/dt.
If we add a low capacitor in series will the total capacitance
decrease so sensitivity will be better?
Then you will lose the main protection offered by the MOV except for very, very fast transient surges.