The answer to the question in the title is, "Whenever Democrats do it."
When it was thought that the Bush administration was engaged in profiling terrorist suspects, or whenever it was suggested that we should profile (which, of course, we should), the left-leaning media got all in a swivet about infringements of civil rights and other such pretensions. Now the Obama administration is actually going to profile airline travelers, though they won't call it that, and you probably haven't heard much more than subdued tsk tsking from the Left:
While trying hard to avoid admitting to "profiling," the Obama administration has introduced new measures for screening US-bound air travelers based on how closely their personal characteristics match intelligence on potential terrorists. Nationality, age, certain physical characteristics, recently visited countries and partial (Muslim-sounding) names will be used alongside the no-fly list to step up flight security.
Here's a rule of thumb for understanding how the Left interprets any security policy enacted by an administration: If Republicans do it it's ipso facto an outrageous threat to our civil rights. If Democrats do it it's ipso facto a perfectly reasonable effort to guarantee our safety.
If these people ever need to supplement their income maybe they should consider stand-up comedy. They're good at it.
RLC