How white?

The new immigration law in Arizona is flat-out racist, but a lot of people have a hard time understanding how the law could ever have negative effects on people not breaking the law. The inimitable Dr. Isis lays it out for you:

This law, an unchecked open door to racial profiling, terrifies me.  Over the last month it has frequently given me pause to realize how often I don’t carry my identification.  I forget it in my desk at work or leave it in my car.  While I will probably never be suspected of being here illegally, I worry for people like my abeulos, who still speak with strong accents, my darker skinned younger sister, and my godson. I worry that this law will become a mechanism to detain Latinos when police have no other cause. I also worry that other states will jump into Arizona’s deep, dark pool of crazy.

But, I especially wonder about the ways my Latino hermanos will try to conform in order not to raise suspicions.  Not playing their music.  Not speaking Spanish in public.  Changing how they dress.  Eating bratwurst instead of carne asada. An entire population of people trying to just pass enough to not get detained.

How white does one have to act to not get detained by the police?