Denim works well. Way less hazardous to occupy, install or demolish and dispose of than rockwool or fiberglass. Probably the best comprimise on natural.
As a performer the rigid foam panels or spray foam are probably best, toxic but soon you will be able to get it without fire retardant and a thick sheet is a tea cup of goo that saves mega
energy over its lifetime and can be in soil contact even.
The problem with all fibre batts is they take on ambient humidity which kills the r value and in the case of fiber glass, the weight ruins its glued structure. I find the denim to be pretty well intertwined without the toxic glues associated with glass batts. Nasty.
Double bubble reflective insulation is less toxic and
water and moisture resistant. Works well as the vapor barier to denim batts.
Mushroom and hemp foams are available, $$.
Depending on climate clay slip and straw might
be nice or just straw.