As I understand the issue to be argued before the Supreme Court by the WTS, municipalities requiring door to door canvassers of any religion to register in advance with the authorities would violate the U.S. Constitution's guarantee of the free practice of religion in anonymity. I'm not saying "anonymity" is a good thing or a bad thing, but I've never seen it literally stated as a right or hinted as a right in the Constitution.
We have rights against illegal search and seizure, which have been lumped under a "right of privacy" umbrella. But it seems a legal stretch to extend this to door to door canvassing or door to door preaching. Registering ones activities with the municipality for the safety and security of it's citizens would seem to be non-intrusive, non-restrictive and of minor inconvenience to the Witnesses. As much as the Witnesses have, in the past, promoted the right of free exercise of religion through court cases, I think they are wrong on this one. Just my opinion.