No amount of prolix explanation excuses even the act of stereotyping.

It depends of why and how you use stereotypes.

Prejudice only properly refers to judgments formed without consideration of the available information

Prejudging is legitimate when we do not have all the relevant facts of an object or subject, having to resort to inductive reasoning in order to try to induce and predict its individual characteristics.

It's all about trying to make new information about someone or something, so we can economize information.