LET'S first examine the issue from a purely pragmatic perspective and put aside the religious associations with the burqa and niquab or any other form of religious clothing for that matter.
If I was to present my self in a bank or Government building or at a country's customs control wearing a baraclava or a full face motorcycle helmet and dark glasses or a handkerchief across my face or a hood, I would expect to be asked to remove the item to reveal my face and therefore my identity or asked to leave. I may be wearing them legitimately in my terms because of some facial disfigurement for example or belief that requires me to hide my face.
But by wearing such an item I am unrecognisable both to the staff, security and security cameras and understandably I would be considered a potential risk to those working in such an environment. Therefore is it not unreasonable to require all persons of whatever faith or cultural background to be treated the same?
In western culture a person's identity is their face and therefore to hide it creates many problems and in some instances presents a threat. If people won't reveal their identity voluntarily then unfortunately laws have to be passed to ensure that they do.
I don't need to be told not to walk into a Mosque with my shoes on or my wife to walk around a country in the Middle-East dressed in revealing or provocative clothing. It would be inappropriate and disrespectful and moreover it would not be tolerated or accepted. If I don't like this then I don't have to visit such places, let alone live in them. If I did I would expect to observe their cultural customs and therefore not unreasonably I expect them to observe ours. I think we call it democracy.