Ok, just for the sake of argument, look at the other side. It's just an address. You ALREADY give them your home address (the one in the real world) AND your fingerprints, and other "personal information".
So, simply asking for it isn't any violation of our rights, that I can see. That being said, what they DO with that information could be a violation of something. Not privacy, since if you're on social media, you're (voluntarily) in PUBLIC, so you don't have a reasonable expectation of privacy.
Government monitoring what you say, in public, isn't any violation of anything. Doesn't affect your free speech rights, UNLESS they try to tell you what you can and cannot say. Then it becomes a free speech issue (censorship). A PRIVATE entity, such as Facebook etc., (or this forum) can set their own rules, and those are not any violation of your civil rights.
They want the government to review your posts to see if you are any threat. Forget free speech, right to privacy etc
This could be an issue, BUT, you need to be clear on what issue it is, and that depends specifically on what the situation is, and who does what.
Monitoring your social media posts is not even remotely the same thing as a wire tap on your telephone. They don't need a WARRANT to read what you post in public chat. Just as they don't need a warrant to go through the trash that you have thrown away. AND its not violating any of our rights when they do it.
Now, here's the risk, suppose they get this (requiring your social media address & account #) as a requirement but don't have the foresight (or deliberately refuse) to set up the system with the flexibility to deal with someone (such as an old dinosaur like me) who does NOT HAVE a social media account.
I can easily see the glee on the faces of the anti-gun zealots when the permit system locks up and denies re-issue due to "failure to provide required information", when in fact you did provide it, but the answer was "none".
Sure, there will be a process for fixing that "technical glitch" but it will take time, probably cost additional money, and may not even exist until AFTER the first successful legal challenge.
Any of that is still a "win" for the anti gun crowd.
Only in NY do we have politicians that want to run your entire life.
No, sorry, we have those in EVERY state. In NY and a few other places they have almost total control of the government, but they exist everywhere.