There's usually much more variation between individuals within a group (say, all white people) than between groups (say, white vs. asian people), nevermind individuals from different groups. Judging individuals based on aggregate statistics about their group would be foolish in the extreme. (Not to mention morally dubious, at best.)
Or course it depends on the size of the group, and you can construct artificial groupings to make the above false, but let's just say that all the 'standard' groups are covered: ethnicity, skin colour, gender, sexuality, etc. etc.
> There's usually much more variation between individuals within a group (say, all white people) than between groups (say, white vs. asian people), nevermind individuals from different groups.
This is statistically illiterate. Let's say you have two sets of random variables X and Y, both from Normal distributions with standard deviation 2, where the mean of X is 0 and the mean of Y is 1. Knowing whether a measurement comes from X or Y will still allow you to make more accurate predictions, even though the within-group variance is larger than the between-group variance. For very large groups, this applies much more so. If you have high-dimensional multivariate data, it is possible to assign individuals to clusters very accurately even if all individual measurements overlap substantially.
This is the real issue: the use of certain stereotypes is a political and ethical debate, and those against using stereotypes should stop pretending there are no costs in terms of sub-optimal decision making. There are defensible ethical reasons for being against some types of discrimination based on valid stereotypes.
Let's break it down by gender, a woman is an order of magnitude less likely to mug you than a man. The difference between groups (female or male) is MUCH larger than the difference in the groups (white male vs. black male or white female vs. black female)
> white male vs. black male or white female vs. black female
These are still groups. I (a male) am much less likely to mug anyone (let's say 1 in a million chance this year) than certain individual women. Within the group of men and within the group of women, the "mugging probability" varies from almost zero to almost one.
Not all stereotypes are true. People have stereotyped others in the past and some of it had to do with other people being accused of being a witch or possessed if they have a medical condition as epilepsy. In Africa, some albinos may also be accused of witchcraft and killed or their body parts taken. As far as people being accused of the supernatural as I mentioned or as being vampires, there's plenty of wrong stereotypes that come to mind. I'm guilty of stereotyping but I also know that man fears what it doesn't know. Sometimes groups make up reasons to fear others because they don't know much about the others and their potential threat levels. Stereotypes are useful for protecting the self and group sometimes but in a public circle (internet) where you make known your stereotype around those that you do stereotype, if it's not true, it's just a given that it'll cause issues. No one cares if you stereotype and keep it to you or your inner circle but it's obvious it'll cause issues in large public forums.
And I just gave a reason why stereotypes can be inaccurate. There's truth in stereotyping and also truth in being cautious about stereotyping because if we want to have a civil society, both frames of thought need moderated.
Edit: Also are we getting the irony that "stereotypes are inaccurate" is a stereotype in itself that has proven at times to be inaccurate?