I think it depends on the discriminatory value of the "profile". If the profile is "male", I don't think it's OK to stop and search every male found, because it's just not enough of an indicator by itself. If the profile on the other hand is "person wearing a neon-green jacket with pictures of lolcats", it seems perfectly fine to use that as the sole indicator needed to stop someone who was to be sighted wearing such a thing.
These kind of issues would be a lot simpler if people were able to use Bayes' law to actually estimate how likely someone is guilty.
There have been way to many discussions with one side claiming using certain kinds of evidence is unethical, and another side claiming the evidence does have some statistical power.
As far as I'm concerned most of those issues would be resolved if people actually cared to check they had a probable cause before doing anything, most objectionably evidence fails that test, and if it doesn't it shouldn't be ignored.
It's from the UK, which I know has a very different situation to the US for race relations, but after 10 years of reform of the stop and search laws (to reduce racism and needless profiling) the UK recently found 25% of all stops illegal. One of the reforms required the police to record the reason for a stop - they either hadn't recorded anything or it was inadequate for 1 in 4.
Given the hugely higher number of stops of minorities, it's easy to see that they'd be identified in more crime - stop 10x more people of a group and you'll find more weed etc.
What hasn't been shown yet is evidence it's an effective crime fighting tactic, and it's easy to see why it causes minorities to distrust the police.
I'm an American and I am not a minority, but I have been profiled and stopped many times over the years. Each time I'm ask if I have anything in the vehicle, and do I mind if they search. It seems one or two younger white guys driving commercial vehicles are more apt to transport contraband. I don't know how effective this is, but it does happen often.
Perhaps, but building a list of all kinds of evidence insufficient to act on would take a lot of effort, and I fear it won't take away the underlying problems.
Telling someone to ignore the fact that group X is Y% more likely to commit a crime is very unlikely to work (since purposely ignoring something is somewhat contradictory). You'd likely get better results by asking someone why they did something despite lacking sufficient evidence.
There is nothing inherently discriminatory in questioning, the discrimination can creep when you build the profile not when apply it.
By definition every investigation technique is designed to be discriminatory in the proper sense of the word since you discriminate using the evidence you have so far.