I disagree fundamentally with your first sentence. There is nothing wrong with a law that protects a small number of relatively powerless women from the whims of a mob. 

What harm does the clothing do to you? I'm not talking here about driver's licences or the right to face an accuser in court. I'm talking about how when you walk around--or get on a bus--and see someone with a veil. What specific damage is done to you? 

If instead the reply is that you are doing it for the womens' own good, because the niqab harms them, in your opinion, consider if you'd appreciate that same principle applied to you. Is it okay if some of the progressives here impose their cultural values on you? I can think of a few, beginning with "respect for..." that I'd like to legislate that you follow!