In my experience a Faraday cage does not need to be earthed with low power signals, in high power shielding they are earthed, but mainly for safety to stop a charge build up on the surface of the cage. The idea with a Faraday cage is that the external signals are routed around the outside conducting material and leave a void inside with no electrical charge. Any opening in a Faraday cage needs to be no larger than 1/8 of the shortest ( highest frequency ) wavelength you are trying to block ( that is why you can see inside a microwave even with door closed because the door has a metal screen with thousands of tiny holes punched into it, light can get through but not longer the wavelength length electrical waves ). Domestic Microwaves work on around 2.5Ghz, and keyless entry works on about 433Mhz, so if the high power ( 900 watts + ) microwaves cannot get out of the microwave cabinet, there is no way the low power 433Mhz ( measures in Milliwatts ) is gonna get in, earthed or not.
Copper or Mumetal or even aluminium works very well for faraday cage, because it is good electrical conductivity rather than magnetic properties that you are looking for.