Thank you everyone.  Question; in climate zone 5 with cold, rainy/snowy winters and hot, dry summers, what type of sheet-insulation subfloor insulation (Polyiso, XPS, or EPS) has the least chance of mold?  Or would forgoing subfloor insulation entirely be advisable for mold prevention?

The flooring will be engineered hardwood, and the underlayment above the subfloor has an integrated vapor barrier (Quietwalk plus). Since the underlayment has its own vapor barrier, would it be problematic for the subfloor insulation (between joists) to be foil-backed Rmax Thermasheath (creating a vapor barrier), i.e. would there be a mold risk from the subfloor being sandwiched between two de-facto vapor barriers? 

More details: due to chemical sensitivities we won’t be using spray foam, so the air sealing will not be perfect.  Also, the contractor indicated the joists are too far apart to attach the sheets to the bottom of the joists, so they would go between the joists.  There will be two subfloors (the 1959 shiplap which is not airtight, and 5/8 plywood/wood-shims on top that we’ll use to level that in preparation for flooring — we won’t be using leveling compound). There will be 1/8 gaps between sheets of plywood, and a ¼ inch gap at the walls (the Quietwalk and flooring will also have a gap at the walls).

This would mean that whatever insulation we use, the shiplap wood subfloor and plywood, will be between the sheet insulation and the Quietwalk Plus underlayment (which has a vapor barrier). 

The crawl space will be vented, but the vents close at 40 and open at 70.

There will be a sheet of 10-12 mil plastic on the dirt of the crawl space. 

3 sides of the basement and crawlspace wall (only the above-grade portions) will have exsulation in the following assembly: 5/8 plywood, Tyvek drainwrap, 1 inch XPS Foamular as exterior insulation, rainscreen, then metal siding, but the concrete foundation will not be insulated.  None of the interior basement or crawlspace walls are insulated.

The home has a ductless heat pump which also has AC (but the AC will be rarely used, and only in the dry hot summer conditions).

There is insulation in the living space, and exsulation on above-ground  basement/crawlspace walls. 

Our main goal is avoiding risk of mold.  Would using the Pinkboard Owens-Corning Foamular XPS (which doesn’t have a foil backing) be safer in that regard than the foil-faced polyiso? Or more risky due to being slightly more porous.  I was considering EPS but so far have not found one that is not foil-backed that doesn’t have a lot of “crumbly” reviews.

I’d love feedback on the best sheet-based subfloor insulation to choose in that scenario, or whether it’s best to avoid subfloor insulation.  And whether there is an installation method that decreases the chance of mold

Thanks so much!