I dont think it matters if there is even a tiny grain of truth in a stereotype (often these 'truths' are based on a misunderstanding of a culture steeped in ignorance of that culture or there may have been a grain of truth in the dim and distant past) Stereotypes are simplistic over generalizations that do not represent most individuals within a group. They generally serve to to enhance our own self-identity and are harmful in that they are the foundation for prejudice and discrimination. They also create obstacles in getting to know people for whom they are versus who we think they might be - if we do this we limit ourselves. They are also dangerous if they sink into the psyche of a group and that group then begins to limit themselves through this stereotype.
Joke stereotypes are no less harmful - take the Barbara Windsor Carry on Nursing character of the 'naughty nurse' - stupid and up for it - perhaps to some this is a joke but its not to the nurse who is pestered by patients who think its ok to stick their hand up her shirt or the guy at the bar who makes stupid lewd comments in some cases it has led to rape.
Stereotyping people is lazy - in the Uk if we want to liv a world of stereotypes we read the Daily Mail - I'm sure there must be an equivalent in the states.