At a minimum, pretty much everything. The cage builder isn't going to want carpet, dash, plastics, etc. It's hard to contort around and it's even harder when there's extra stuff in the way. Also that stuff will catch on fire and/or melt when they are trying to weld and give off nice cancer smoke. I'd recommend stripping it and reinstalling everything after the fact. I know it sucks but the shop who is building your cage will charge you way less if it's already stripped.
I'd also highly recommend shelling at least the driver door so the door bars can fill that void. You want the cage (especially around the driver seat) to be as spacious as possible... it's safer, makes adjusting lap belts easier, makes repositioning the seat easier, and is more comfortable. The PO of the 735i didn't gut the driver door before caging and even though the car is huge, the cage in our miata (with gutted doors) feels roomier.
Full Ass Racing
#455 Piñata Miata - 1990 Miata
#735 BMDollhÜr 7Turdy5i - 1990 735i