Urushiol toxicity comes from the immune reaction it generates in about 60-80% of the population. However, urushiol doesn’t spark an immune response on its own. It turns your body against itself. Immune responses are aimed at antigens (not born of, so not self), but urushiol breakdown products are haptens (to fasten to); think of them as half antigens. Haptens must combine with something else to become full antigens. In the case of urushiol, they combine with proteins from our own cell membranes.
When portion of the urushiol combines with the integral protein, now the protein is seen as foreign and your immune system might start to attack, in a process called type IV delayed hypersensitivity. This produces inflammation and tissue damage in a reaction termed allergic contact dermatitis.