It turns out that stereotypes, however distasteful, usually do have a certain degree of accuracy: http://heterodoxacademy.org/2016/03/30/are-stereotypes-accur.... You may not want to live in the world where they do, but that reality is what it is.
When you ask people to deny the evidence of their own eyes, you're setting up a kind of resentment that can lead only to bad outcomes.
Of course, it'd be awful to be individually assumed to be a thief because you come from a group full of people unusually likely to be thieves. My point is that if it's a matter of fact that people of that group are more likely to be thieves, whatever the reason, and you tell people that, no, that group isn't full of thieves, and people are terrible for thinking so, then as soon as some demagogue acknowledges the truth, people will run to him no matter how bad his other opinions and no matter how ruinous his policies.
People hate liars, and even more, they hate being compelled by social forces of shame and ridicule to deny their true beliefs. It's better to have an honest conversation about these things than to repress them and create the kind of pressure cooker that explodes and makes a Trump president.
In an EU context, maybe it'd have been better to accept some restrictions on freedom of movement. Maybe it'd have been better to scale back centrally-imposed regulations on consumer goods (e.g., the EU banning traditional UK tea kettles).
Now we're going to see the EU damaged because well-meaning people tried to bring about the world they'd like to see by demanding everyone pretend it be so, and only children play pretend.