Great question — answering as the UphillTech team:
To me, it seems like high-quality USA-made rockwool batts with no backing, and gypsum board with no backing, would be the lowest risk for mold or other air quality problems. Fiberglass seems risky if there ever were moisture, such as from condensation. It also seems like rockwool is easier to maintain - firmer and less dusty, while fiberglass is more likely to settle overtime and be a dusty mess during any repairs. Also, the contractor suggested fiberglass with paper-facing, but I imagine unfaced batts (of either rockwool or fiberglass) would be best for breathability/dryability, it's just that rockwool doesn't need paper to firmly fit in cavities, whereas fiberglass is easier to install...
Full answer by cr0: https://diy.stackexchange.com/a/301766 (CC BY-SA 4.0).
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