The problem with moisture in your home is not when it gets in or gets out, that's inevitable, but when it gets trapped. And that is where you need to be careful with poly sheeting as it tends to trap water and not let it move in or out. I found out the hard way when I tore down the walls in my basement bedroom to find they insulated by stapling plastic sheeting over paper backed insulation. The plastic sheeting trapped the moisture against the paper face of the insulation and I had a nice film of black mildew all along the insides of my walls.
Mold and mildew need two things - water and organic material to feed on. If you put poly sheeting against something like wood or paper, the trapped water provides steady moisture while the mold and mildew enjoy the wood/paper.
It can be costly or tricky, but the best thing to do is to create a humid environment for the iguana that is separate from the room and in a container that will not be affected by the moisture.