Most if not all Boolean operations in 2d (+3d) expect shapes not lines. Proof: Select grid, go Path->Stroke to Path - add-select "irregular" object and go Path->Intersection - voilá.
Or if you don´t mind "invisible objects" select Grid+Object and go Object->Clip->Set.
I want to create a grid then place an irregular object in the grid and use the object profile to create a hole in the grid, but they keep disappearing
Workflow
Most if not all Boolean operations in 2d (+3d) expect shapes not lines. Proof: Select grid, go Path->Stroke to Path - add-select "irregular" object and go Path->Intersection - voilá.
Or if you don´t mind "invisible objects" select Grid+Object and go Object->Clip->Set.