On the surface, such a request seems innocent enough. But it also implies that I might be a criminal. I don't like being made to feel like a suspected criminal while I intend to buy something at your store. Besides, what if somebody steals my bag? Or the punk behind the counter rifles through it?
As such, I refuse to shop at any store that requires me to remove my bag.
Society these days seems willing to put up with an awful lot of little inconveniences for other people's security and peace of mind. Are we ok with being treated as guilty until proven innocent? I think most people would say no. But we allow it every day.
We put up with it at a much larger scale too. Apparently now there is over a million names on the US terror watch list. One million names. Added with secret criteria, and impossible to remove. If you are unlucky enough to have a similar name as somebody who may have possibly had a connection to something that might have maybe been a possible terrorist action, your flying days will become very difficult. You can't defend yourself against the accusations (since you don't know what they are) and you can't fight the label (unless you have a lot of money for some lawyers). Guilty until proven innocent... but you can't prove innocence.
Being a shoplifting suspect and being a terror suspect are certainly several orders of magnitude different. But they follow the same principle: give up your rights for the peace of mind of somebody else.
Are you willing to be treated like a shoplifting suspect for the peace of mind of the shop owner?
Are you willing to be treated like a terrorist suspect for the peace of mind of a country?