Having public conversations and having cops insert themselves is.. actually really well established case law. Yes the cops can listen in when you have no expectation of privacy.
We don't want cops having and abusing backdoors but "playing the game" is perfectly legit. The cops do not owe you some sense of playing gently.
I'm not sure this is the sentence you meant. Of course anybody can listen in when you have no expectation of privacy. Without a court ordered search warrant, they can't listen in when you do have expectation of privacy.
If a cop were to gain entry, or have a paid informant gain entry, whether by paying a cover, or bluffing association with a regular, that seems well within the law.
This is not someones house, or your bedroom, or the cops picking a lock & busting down a door. Social media is just an online "third place". It is not work, it is not your home, it is not private.. it is public square, even if you mark yourself "private" and only accept 200 followers instead of 300.
Facebook is not private, neither is Twitter, especially not the profiles on Facebook.
You can have whatever wishes you want, but if you are behaving inconsistently with the truth, you're going to spend a lot of time being wrong and having your wishes disobeyed.