It appears that dupes with "Unconstructive" trait are completely incapable of taking any part in construction, not just performing the building errand. I happened to have my digger unconstructive, and it completely prevents her from performing "construction dig". It makes any projects on dense materials a chore, since I have to manually request a dig and schedule construction after it's done.
By the way, it may or may not be intended, but delivery jobs are similarly obstructed.
1. Have a dupe:
- With "Unconstructive" trait
- With skill points in digging (bonus points if it's your only miner)
2. Request construction on a hard material
3. The resources will be delivered, but this dupe will not be able to dig out the construction zone with "not allowed" errand status.