Is racial profiling against Muslims morally permissible under any circumstances? If so, why?

I wonder if you meant "impermissible" rather than "permissible", but either way I'll try to address the question. With respect to any ethical principle, at almost any level of abstraction, it's hard to say that it applies under literally any circumstance (maybe "do the right thing" is an exception, but it obviously doesn't help much). "Never torture innocent children" seems a pretty secure principle, yet it's not hard to devise a situation in which maybe one has to violate it - say the fate of millions of lives really depends on torturing this one child. (Leave aside how you can know that this is so, a real problem for alleged "ticking bomb" scenarios.) So I would say any kind of racial profiling is wrong because it violates certain basic rights, especially the right to be treated with dignity and to be treated fairly under the rule of law - which means that you have to have specifically done something to be singled out for negative treatment. But like all rights, this one too can be swamped by...