Reading public messages seems like a super reasonable thing for the police to be doing, to keep tabs on groups that have recently engaged in disruption and violence. Whether those groups are right wing or left wing.
I don't see how you can prevent the police from reading stuff that's being broadcast for everyone else to see.
And threats of violence, or evidence of organizing to cause violence, should be investigated.
The police aggregate vast sums of data and uses it in ways that the public does not understand, intend, or expect. It's not unlike the way people 'sign' away their privacy on the internet without being aware that their data will then be sold and resold and used against them.
It is a common belief that information is a weapon, and it certainly can be used as one. So does it makes sense, at least from one perspective, that our information should not be legal to catalogue? After all, it is illegal in the U.S. for the government to create a registry of firearms owners because such a registry could be used against the people and its very existence would be an infringement on the rights of those people.
If a police officer sits down at the dinner table next to me and listens in on my conversation with friends and family, I'd be quite uncomfortable. I'd feel equally uncomfortable if they sat across the restaurant and pointed a microphone at the table to record everything. However, suddenly we treat them like normal people if they download the entire contents of our digital lives and process every word we've ever written online.
It's one thing for Twitter to be accessible to natural persons publicly. It's another for a government to treat everyone as though they are under investigation at all times, without a warrant.
For clarity, in my opinion, a police officer who just happens to follow me on twitter because he likes video games is a natural person. However, he stops being a natural person once he starts representing the organization he works for.
Innocent people should not be surveilled ruthlessly on the off chance that every now and again we catch one evil person. In my mind, it's like the TSA invading everyone's privacy without ever catching a single terrorist. It's a waste of resources, on top of being a disgusting behavior.
On the other hand, there are tons of cameras in public spaces too. So, even though people have had a built-in expectation of ephemerality, that's already been violated for quite a while now.
There is an ocean of options in between “do nothing” and “surveil and database every citizen who potentially maybe, might, could exercise their constitutional protections and protest.” A vast amount of options.