Even if you accept the proposition that proportionally more of Group A** might be expected to commit crimes than group B, there are at least three instant flaws I can think of: firstly, the statistics are dubious in and of themselves -- let's face it, even if you assume the best of intentions, most people only *think* the know the data about this sort of thing, and their judgements tend to be wildly wrong, or at least poorly-researched. Generally, people's knowledge of and ability to interpret statistics is not exactly world-class (if you think about it this has to be true by definition).
Secondly, even you can establish a correlation between Group A and some undesirable trait, then it's unlikely to be a causal link if the characteristic of Group A is defined so vaguely. A name isn't enough to determine someone's character, nor is a photo, nor is the first few seconds we tend to take to form our first opinions of someone we hadn't previously met. So it's still an unjustifiable bias even if the correlation exists.
Thirdly, Even if you can set aside the idea that the statistic is only imagined, or show that it's a semi-justifiable claim given enough people, most companies wouldn't hire enough people to justify such sweeping biases -- so given two identical CVs the idea that one should be dismissed while the other accepted merely on the basis of the name atop is a clear example of poor judgement that has no grounding in logic.
Fourthly, we're really talking about conscious biases at the moment. Presumably the scenario that Naomi and v-e are envisaging is that an employer is fully aware of what they're doing -- and perhaps that's even true more often than I'd care to admit -- but, in the example of CVs, the employer will have seen the identical CVs under different names but genuinely and honestly reached the conclusion that the CV with the "white" name is a higher quality than the other one, without ever giving thought to all this argument about whether the statistics would or would not justify his decision for sound social or economic reasons.
Oh, and thinking about it, what's this nonsense about Jims being almost certainly upstanding citizens that merit no such judgements? I'm flattered, of course, but it's still based on what exactly? It's the textbook definition of white male privilege to even make the suggestion.
I want to move away from the specific topic of whether bias against Muslims can be justified. It can't, but even if it can there's a far wider issue here.