I just come back to "probable cause". Any search without a warrant is bad, and to get that warrant you should need to show that more than half of those you search have the specified contraband. That's what "probable" means, after all.
Bayesian reasoning tells us that's a remarkably high bar to clear based on any sort of profile, but it's technically possible. If, say, you have good evidence that more than half of those who visited Silk Road have illegal drugs in their house right now, then, OK, that's a legit reason to search the houses of everyone who did.
But most profiling and broad searches are closer to 0.05% than to 50%. Search all the computers in the state and find one guilty? What percentage is that? Stop 1000 people at a sobriety checkpoint for every drunk you find? Well, that's a bit less than half, now, isn't it. Search people who fit a profile because they have a one in a million, instead of 1 in 100 million chance of being a terrorist? "They're 100 times as likely if they fit!" Yeah, well, 1 in a million is less than 1 in 2, so keep working on that profile buddy.
Probable cause. It's a simple concept.