You aren't supposed to install Polyiso in your house without putting something like drywall in front of it in order to meet fire code, unless you're using something like Dow Thermax which meets fire code by itself. Generally speaking, could I put mineral wool over the rigid foam board instead of drywall?
It’s complicated. Actually, the Code says “foam plastic insulation” must meet a flame spread index of 75 and a smoke development index of 450. (ICC R316.3) However, there’s an exception for loose fill insulation and insulation more than 4” thick.
So, if the product you are using exceeds these values, you can cover it with various materials, including 1 1/2” min. thickness of mineral fiber insulation. (See ICC R316.4.3)