Perlite is a reasonable and common insulating material. I have two dump-truck loads of used medium that I got from a
local hydro tomato guy. By the truckload it is relatively cheap even if new, the used stuff I will use for a pizza
oven,
solar pottery kiln and, after that, a
solar forge. I do not believe that it qualifies as organic although it is pretty much just fluffed rock, but recycled perlite might be a possibility. ESCS (expanded shale, clay, slate) was once a promising insulating material and lightweight aggregate, have not heard much about it in years. A product that is, again, not organic but a quality product is reflective bubble foil. In a properly detailed installation, the foil reflects and returns heat and increases the r-value of any kind of dead air space to optimum (no drafts or leaks and air will insulate great).
In old school rustic construction, pretty much any locally harvestable grass/hay/straw was called browse and was used to stuff, chink, insulate, waterproof, and bind together whatever was available. I have heard of heath or heathers being used as a sort of nest insulation for very simple dugouts. any kind of fluffy material would work for this. with a modern chopper/shredder type of setup many types of organic waste could be processed and treated with either slip-clay or borate/other salts and used as a compacted stuffing, make into pressed tiles or blocks, whatever.
In the realm of more chemical, non organic insulators, lightweight aerated cement (foaming type) blocks are available. they can be cut with a standard saw, high compressive strength, easy bonding system (mortar roller not trowel) and a few other benefits. Still a better system than using masses of
trees to build, and does not use nearly as much high
energy input portland cement per unit of size and structure as traditional blocks,
concrete, etc. i am not referring to pumice or lightweight standard (hadite) blocks but to chemically foamed cement. of course, lightweight blocks such as hadite also have some insulation value and are commonly available as well.