Quasi Real is Real Enough for Me
The Spell descriptions sometimes say "quasi-real", which can implicitly lead one to conclude that if the thing imitated is intended to have mass, it does. Explicitly, it is not a necessary condition for shadow spells to produce mass, as force spells do not produce mass and can imitate effects like gravity (Reverse Gravity) or a Wall (Wall of Force). We could think of the shadow effects as a play of forces. I once proposed shadow magic could be like a 4th dimensional object's shadow, with the force acting on objects in the third dimension at imperceptible angles.
I once asked my physics professor about how much force was produced by an impervious force field colliding at 100 meters per second, and he asked what the mass was. I said zero, and he said the answer was also zero.
One of the shadow spells uses electricity as its example. This is where it gets tricky. Things like electricity and acid inflict a kind of damage that comes from a substance (electrons) interacting because of the structure of that substance. A force field by itself would have to be complex on some subatomic level in order to imitate, but not literally be electrons. Which, Occam's Razor leads us to believe the simpler solution is the best - that some of shadow magic is real, and has mass, because it would be harder (and unnecessarily complex) for the spell to replicate so many effects without it.
So while we could easily imagine force fields and static and magnetism, etc. as source of shadow damage being partially real, it stops making sense when you replicate a Black Dragon that stomps on the Barbarian and Spews Acid all over the Paladin's Armor.
Quantum Shadow Stuff?
The one tricky line is this:
Nondamaging effects, such as Gust of Wind, have normal effects except
against those who disbelieve them. Against disbelievers, they have no
effect. (PHB, p.277)
No effect? That's directly inconsistent with the 20%-80% rule for spells like Shadow Invocation and Shades. Shades is a 9th level spell that makes things 80% real. If you disbelieve a bridge that is 80% real, can you cross it or do you pass through? If a Wall is 80% real, and you successfully disbelieve it, can you walk through it?
This appears to imply that the Shadow-stuff is semi-intelligent, and reacts, withdrawing itself from disbelievers, sort of like a shadow version of the Double Slit experiment: the Shadow-stuff is only where you need it to be when you don't look to see if its really there, but if you are skeptical and focus on whether it is there, it isn't.