Stereotypes never fit anyone perfectly. So using them for interactions will cause subtle errors. But in close relationships ... the closer a relationship is, the smaller the errors that are tolerated. So in a sufficiently close relationship, those 'subtle errors' will seem large and intolerable (and 'subtle' will take on a new meaning, which we might have called 'minute' before). Therefore we should avoid stereotypes in close relationships.
By the way, not using stereotypes, when you don't know someone well, is bound to create errors too, because you don't know the person well enough to act error-freely towards him. In this sort of situation, stereotyping can be considered an error reduction strategy! (Of course the stereotypes must always be held tentatively.)
This logic works in close relationships too. We don't know people perfectly, so there will be error. Why, then, are stereotypes bad in close relationships? Well if there were literally 2 billion of them, with slightly different shades of meaning, and we used those, it might be ok even in very close relationships (but there would be a point at which 2 billion was too few). But as it is, we only have fairly general stereotypes, which will cause a high error rate in close relationships where people ought to know more detail than that.