Why does tomato sauce stain clothes?

The stain is produced by the carotenoid pigments from the tomato that are mobilized by being dissolved or suspended in the oils in the sauce. In that form, they will penetrate into the threads of the cloth and resist removal by any but the most aggressive detergents that can emulsify the oils and solubilize the stain.

Marinara sauce will stain clothing really well...Never wear a white shirt to an Italian restaurant.