Not necessarily.

Yes, if you want owning a firearm to remain a right.

We don't decide whether to approve any governmental actions based on rumor or who has a "rep" at a school. But you'll never be able to condition permission to exercise a constitutional right on such things. We're not going to take away someone's ability to buy a firearm based on whether people think someone's a little unhinged. If a "red flag" law is going to be implemented, it will have to be much more formal than that - an actual investigation that culminates in a formal decision-making process that the individual is notified of and has an opportunity to participate in, and very likely some kind of judicially-overseen hearing with medical testimony.

There's almost zero chance that we'll set up that kind of system just to have a "no gun" list - it would be an enormous amount of bureaucracy, and unless that bureaucracy was really well funded and really aggressive in investigating people, would be mostly useless. Audrey Hale didn't do anything that was so significant that any such system would bar a firearm purchase before they bought the weapons - quite some time before the hotline calls. It would take weeks to get someone stripped of their ability to buy a firearm in even expedited cases - months and months, in ordinary cases.

Again, unless you want to switch to treating firearm ownership as a privilege, not a right.