I think it's more complicated than that: a country can't become self-sufficient in the long term if the majority of its population either flees or starves to death in the aftermath of an ecological disaster. You need foreign food and medical aid in that sort of situation, because your domestic capacity can't possibly grow to fit the needs.

Similarly for little things like soap: they're essential for basic health, but economically they fall into the "discretionary purchases" bucket. If the people being supplied by this nonprofit don't have the discretionary income to purchase locally-manufactured soap in the first place, then you're not curtailing any amount of domestic industry by providing it to them for free. Counterintuitively, you're promoting long-term domestic economic security by ensuring that more children make it to productive adulthood.

(All of this not to say that things like clothes donation's can't hurt the recipient's economy, which they certainly can. But I don't think that cynicism is warranted in this case.)