Photoresistor value drops when board stacked on Arduino Uno
It should not happen.

I have changed this answer, because at first I read that the resulting value was changed by -40, but I think it drops from 900 to 40.

The shield is doing something, so it is not empty. Perhaps it shortcuts the AREF to GND. Perhaps you are reading an open input, and the sensor is at another analog pin. Perhaps the shield does something to the voltage pins.

A breadboard can have bad contacts. The shield can have bad contacts.

Be sure that the sensor is connected to the channel that you are reading. Measure the voltage at that analog input with a multimeter with and without the shield. Check the 5V, 3.3V and AREF pins with and without the shield.