There is a vast difference between a Christian desire for privacy and the unbelieving desire for anonymity. But this requires some teasing out, which I can only just begin here.
First, let me make a few observations that would indicate that we don't really know what privacy should mean. Vast regiments of people post things to the Internet that they shouldn't, and if, say, the pastor of a church said something to one of his young men about the most recent inappropriate thing, and that admonition became controversial in the church (or within the youth group), the chances are good that the indignation would be fueled in part by the view that the young man had had his privacy invaded. But what are we talking about, privacy? He posted the dern thing on something called the worldwide web.
Here is another example. Before proceeding, let me go on record as agreeing with Charles Krauthammer that the deployment of drones over domestic airspace is Obnoxious, and the first public spirited Americano who shoots one of them down should be awarded the Medal of Freedom. Clearly this is a tyrannical move, and we shouldn't like it at all. But, that said, public cameras in public spaces is not an invasion of privacy.
If I am out in public, it is not an invasion of my privacy if people see me. If I am standing on the corner of Third and Main, how is it an invasion of my privacy if someone takes a picture, and it turns out I am in it?
If militarized cops with automatic weapons are stationed in public places every fifty feet, and this happens for no good reason, there is cause for alarm. But nobody's privacy is being invaded. That may well happen, but it hasn't happened yet.
I don't like the Brit system of surveillance cameras everywhere, and believe them to be incipiently tyrannical -- not because the state in such cases wants to multiply evidence, but rather because of their natural tendency to want to monopolize control of such evidence. There is a vast distinction. This is connected to those various police departments that are conducting a war on photography. I like the fact that cop cars have dashcams on them, and I like the fact that if someone is arrested in a public place, there will likely be scores of privately owned phone cameras recording the events.
To demand privacy in public places is actually demanding anonymity. And anonymity is not the enemy of tyranny that it pretends to be.
To ask that the state have sole control over all such cameras is to be at war with the biblical requirement of two or three witnesses. To demand that no one be allowed to record behavior in public places is also to be at war with the biblical requirement of two or three witnesses.
Now all this presupposes the existence of private spaces, the boundaries of which should be clear, defined, and defended. More on this later.