To people who say stereotyping is wrong, I would simply ask: Where do you think these stereotypes came from?
If we accept that society doesn't generally accept new ideas or concepts except over a long period of exposure to them and significant factual evidence to support it, would it not stand to reason that we've come to believe things about people based on the aggregate of data and anecdotal evidence passed on over many generations rather than pure guesswork or single-minded bigotry against a particular group? Everyone is always quick to refer to someone they know who isn't living up to the generalizations often made about their race or ethnicity, but can they produce 50,000 such cases or just 1 or 2? That's the fallacy of personal experience liberal engage in regularly when conversing with others who don't share their one-world agenda.
We're not all the same.
Blacks do, on average, act impulsively under stress and run from authority figures or defy their instructions. Whites do suck at dancing, lack a sense of fashion (ever see them at golf courses or tourist venues, particularly the khaki-short and sandal crowd?), and can't sing a decent rap or blues verse to save their skins. Asians really are stingy, lack basic social etiquette when interacting with people outside their culture especially in retail settings, and are notoriously hard to read. Native Americans do drink to excess, abuse drugs, ignore the countless opportunities and breaks given to them by disingenuously compassionate (white guilt-ridden) governments, and end up in jail out of all proportion to their numbers in the population. Hispanic women really do get triggered easily and kiss their crucifixes whenever they want their fictitious deities to bestow luck and protection on them (while failing to explain what makes them special enough to deserve it).
These things exist for a reason. They're the result of decades, if not centuries, of observation and collection of statistical data. Look around America's prisons - they're half full of Black inmates. Why? Were they all wrongly convicted, and if so, why are they still incarcerated?