I only say nay based on this. What if a red haired male robs a liquor store? The cops should be well within their right to profile all red haired males that cross their path. The same would be true for a hispAnic with a mustache.
But do they have the right to profile just for shots and giggle, absolutely not. The key word is use discretion and not abuse of power. All the Supreme Court rulings in the world are not going to be able to stop that