I take it you don't mean legal freedom of speech. There's no government entity involved in this.
As for colloquial freedom of speech on the internet, that opens up a whole can of worms.
In a general sense, anyone has the power to out anyone else. The platform that it's on has the power to broadcast that information as widely, if not more widely, than a cable news network.
Will there be rules on anyone outing anyone else?
Will news organizations be held to a higher standard of NOT investigating people's backgrounds? Will CNN be held to a different standard than even the rest of the other journalists?
Then there's the line between investigative reporting and outing. Where does that get drawn? I remember the case where someone posted on their Facebook account a picture of them holding up a dead cat with an arrow in its head. People found out her workplace and had her fired within a couple days. Her name and personal details were printed. Should news organizations have printed her personal information?
In this particular case, CNN declined to post personal details. When some people saw the reservation to print personal details as blackmail, CNN clarified that it meant that the reservation wasn't contingent on the apology, but that the statement that personal details wouldn't be printed wasn't a blanket statement. From the comments I've seen, very few people took that at face value.
On the other side, CNN's staffer's were outed with personal details of their families. That it was done got press attention as well. That seems to be getting a lot less censure, or maybe the censure is assumed.
For the most part, I don't see people who criticize Trump who are also trolling with views they don't really hold. Most of them seem sincere in their criticism. And many of them are getting punished for their views. Like the woman who worked in a bank that a republican congressman told the owner of the bank that this woman was against him. She lost/left her job.
In these very divisive times, there's lots of condemnation to go around.
Besides being ineffective, condemning CNN is inconsistent to me.
I reserve the right to condemn CNN at a later time If I don't like what they do, though.