First of all, I think it's good you bring this up. Better to discuss such matters openly than to pretend they don't exist.
One should be clearer, perhaps, about the step from belief to action. Surely many things correlate with race, gender, or religion; and we may notice these correlations and form beliefs about them and perhaps even test these beliefs through large-scale data collection. In some case, the mere researching of such correlations is morally dubious, by fostering contempt for a group even while serving no legitimate social purpose.
But in the case of crimes, there is a legitimate social purpose: deterrence and apprehension. So it is hard to deny that knowing more about the people who tend to commit certain kinds of crimes can be useful. But then how useful such knowledge will be depends on what one would be able and morally permitted do with it if one had it.
In the case of serious crimes there is, I think, a clear presumption in favor of using such knowledge and hence of acquiring it. If those who commit a certain kind of serious crime in some city are described (by the victims and witnesses) as predominantly fitting a certain profile, then it makes sense to concentrate scarce police resources on people fitting this profile. To take an extreme example, if virtually all rapes and attempted rapes in some city are reportedly committed by males, then it makes little sense to have half of the plainclothes anti-rape task force trailing females.
Criminal profiling of African Americans is different in three important respects. First, insofar as correlations exist, they tend to be much weaker than just described. Second, there is a long-standing history of severe discrimination and disadvantage the ongoing social and psychological effects of which racial profiling is likely to aggravate. Third, those engaging in (perhaps expressly authorized) racial profiling may have a certain degree of racism that may influence their racial profiling in ways that unduly harm African Americans and in turn deepen the profilers' racism.
These three considerations may typically be weighty enough to disqualify most actual racial profiling that has taken place. But I don't think they can show that racial profiling is wrong in principle or even merely always wrong in this country. There may be cases where racial profiling is likely to be highly effective in reducing serious crime even while its cost are much lower than usual. For example, consider a city that is racially mixed and where blacks are highly overrepresented among those who commit and also among those who fall victim to a certain crime. Suppose a special task force is formed to combat this crime, and suppose it is an all-black force. In this case, the three considerations against racial profiling are much weaker than usual, and it is certainly arguable that racial profiling can proceed so long as it really does prove highly effective against the serious crime in question.