If you post public information, it's publicly consumable, including by government intelligence services. If you have a problem with that, consider that the issue might be your choice to post information publicly that you don't want the FBI to see, rather than the fact that the FBI is looking at it.
This sets a dangerous precedent. By letting a government authority to oversee the activity, even if considered public, is still personal. Its a step closer to the cliche - "In Soviet Russia TV watches you"
Congratulations: you are now living in a police state.
"Seeing it" because it's public and "monitoring" it systematically are two very different things.
This isn't like the FBI setting up surveillance equipment to capture and monitor conversations; it's like the FBI asking to look at the tapes that people are already gleefully making and leaving around in public bins for others to pick up and watch.
I get the reasoning - and honestly, it was my first instinct on the news as well - but I don't think it's a direct analog.