Actually, straw bale is a natural material that shields emf’s quite well. I have measured the microwave radiation outside of a straw bale building and then inside and compared. I would have to look up the exact numbers, but the reduction was dramatic.
This was a house that used bamboo to stabilize the straw bales rather than chicken wire, which is what a lot of people use. I have not had the opportunity to measure them, but I would bet that cob houses would also provide significant shielding as the walls are very thick and made of clay and straw. Dragonboard seems like another alternative, but probably much more expensive.
I had an interesting experience the other day while taking measurements in a very rural area. My readings were very low until an airplane flew over, then dropped again after the plane passed. This was not measuring radar, but microwaves in uW/cm2.
Good luck on creating a safe living space.