jurs:
How long are the cables from the Arduino A0-pin to the shields buttons and resistors?Probably long cables crossing other cables with mains power or chhanging currents, and the cables are catching electrical interference, so that no stable analog reading is possible.
With the LCD Keypad Shield directly stacked on the board, cable lengths are short und signals from the button to the A0-pin are undisturbed.
2 short cables routed through bread board, but it does cross the RFID's serial1 cable, and the RTC's I2C cables
Thanks for all your trouble, at least I know where to look for the problem now.