Why is it that the mould that grows inside certain cheeses is safe to eat, but the mould that grows on other things (ie. dirty plates) will make you sick?
Some moulds produce toxins - most don’t. It’s unlikely that the mould on dirty plates will make you sick. It’s possible that bacteria that have grown on the plates alongside the mould will make you sick. Mould in a household setting may be seen as a proxy or indicator that food isn’t in fit condition to eat, rather than being dangerous in itself.
For the same reason that some mushrooms are edible and others are toxic. It’s just the different properties of the different organisms.
Many non-edible molds that appear on aging food aren’t toxic and probably wouldn’t make you sick, although some are very toxic. But the visible presence of either indicates the age and condition of the food is also a hospitable environment for other, possibly invisible toxins.