People seem to think social media is akin to private communications where it's more akin to the public square. Making your IG/FB/whatever profile private doesn't change that.
In NYC for example, there's been a large uptick in teen shootings, many adjacent to schools, and a lot of it involves the idiots posting on social media before & after. One tool could be simply scraping social media for these postings. Another alternate, pre-internet tool was stop&frisk.
While you have a constitutional right to not be searched without consent/probably cause, you do not have a constitutional right to spouting off in the public square without consequence. What you say publicly can & will be used against you in the court of law.
Putting out an IG post of yourself with illegal guns or inciting a shooting is no more private than printing out posters of the same and putting them up around the neighborhood.
Actually, in the U.S., you literally have that specific constitutional right.
The First Amendment protects "spouting off in the public square without consequence" via the Freedoms of Assembly (the right to gather), Speech (say what you like without consequence), Religion (believe what you like), and the right to petition the government.
Loud complaining or even vague and non-specific threats (such as "I'll make you pay for this!") are actually protected by the First Amendment.
There are very rare and limited exceptions, such as "directed to inciting or producing imminent lawless action and is likely to incite or produce such action".
like I can say what I want, but if I say "I DID CRIMES" then guess what.. that could be used as evidence that I DID CRIMES
“Spouting off” is an idiom that can also mean “speaking without a filter” and that’s what OP meant in this case.