a simple hat probably won't make a huge difference. But, the previously shown headgear (what one would call the item in image two, I have no idea.........) does hide unique features that are useful in identification: ears. If you don't think ears provide significant identifications properties, then you've never seen Mr. Spock, H. Ross Perot, or B.H. Obama.
Can anyone really say these ears aren't unique? :
I think not.
But, some of the local Somali-Americans (Somalicans?) feel it's an infringement upon their religious practices to remove the hijab for the purposes of identification. And I agree with them, it is an infringement. Much like it's an infringement of my religious beliefs when I have to swear that I will faithfully something something something, so help me God. But guess what. You Don't Have A Right To A Driver's License. Nor are you required to have a drivers license or drive. So I suggest that if you wish to have your dolshe and eat it too, you're out of luck.
Like it or lump it.