One of the more sane elevated rights police officers have long enjoyed is the right to extreme privacy - their phone numbers and addresses are unlisted by default and sharing the private information of an officer with malicious intent carries a more serious penalty than an equivalent action against a regular individual. Police officers face an elevated level of danger in their personal lives from persons they've arrested or interacted with - if you could spin this website as providing information that makes it easier to identify and harass problematic officers (even if they deserve a significant amount of scrutiny) you'll likely have a strong case to have the site shutdown.
Most people these days seem to be confused about what the term "secret police" means. It doesn't mean a police forces that the public don't know exists. It means a police force that has as some of its members, people whos identities are secret. You know, like the NKVD or STASI.
I was taught as a kid 30 years ago, during the cold war, that having a secret police was a key indicator of an oppressive regime. What you describe as "sane elevated rights" was something I was taught that we needed to fight tooth and nail, possibly with nuclear weapons.
I guess times change. Sometimes I feel like crying.
I suppose the Supreme Court will have to rule on the issue of blurring our badge numbers during the course of a protected activity.
But this does seem related to the constitution through the First Amendment.