Turbans etc, no issues with them at all. They don't cover the face!
Yes it's not being able to see people's (women's) faces that I object to. I come from a culture where people show their faces and I want to continue living that way. Like I value a culture where men cover their legs! 
Someone wearing a burka is scary for children. I was delighted when that daft teaching assistant in Yorkshire (I think) was sacked for insisting on covering her face. The reading of the face (I don't mean speech) is an important way in which we communicate. I don't think I'm being unreasonably intolerant. Nor does French Law. I wish it was the Law here too.
I associate the burka (not hajib) with people who do not want to partake in the society I live in, and I object to that. Strongly.
I accept, reluctantly and not quite whole-heartedly, that women who wear the burka do so voluntarily.
Also (anecdotally) we live in the most security camera saturated country in the world . Crimes sometimes do seem to be solved by CCTV's all pervading presence. Doesn't the burka make a nonsense of this? If a woman in a burka were to be a hardened shoplifter, she can't be identified (and she has somewhere extremely commodious to conceal items!) btw I am not accusing all burka-wearers of being shoplifters, of course they're not!
I'm surprised more people here don't agree with me. Are you all being totally honest?
btw there are plenty of nuns out there but, as someone said, they tend to wear modern dress these days.
Eariier comments. I've never seen a bride with an opaque veil, always transparent. And rarely worn in public, usually just in and around the church. I have absolutely no objection to what anyone wears in private.
I've never seen a nun who covers her face.