ANY infringement on rights will need to be imposed by due process. An arbitrary list of any variety will not do. No-fly list? No way. A single psychiatrist says you're too crazy to own a gun? Nope. Perhaps temporarily (48 hours emergency) followed by hearing(s). And not just because you meet the definition of a mental illness. There must be a credible threat. Or your immediate ability to reason must be impaired substantially (as in psychosis). And there must be a meaningful way to remove the restriction once you have recovered (yes, a number of things can cause a temporary psychosis, including alcohol/substance withdrawal and even "mundane" things like corticosteroids). You can't just say someone has depression or anxiety and in a blanket fashion dispose of their rights.
Violent felons - sure, take away the right. No problem with that, so long as a conviction is won. IOW, a simple accusation doesn't cut it (though I would be good with temporary pending trial if charges are filed and even temporary and limited time frame on domestic violence until a hearing is held on the right to bear arms question).
I would also be open to limits on magazine sizes and banning devices that allow simulated auto fire (bump stocks).
On the other side of this, we make it easier for law abiding citizens to carry in most public places and to travel with their personal weapon. Would anyone advocating control measures be open to anything like that?