Valid concerns, it seems to me, especially since Trump supporters are known to be mentally defective deplorables.
In liberalism/socialism's shifting sands, what we think is reasonable ("due process" "adjudicated mentally defective") is gonna be my next door neighbor or ME down the road.
"committed to a mental institution" -- could be argued to include a hospitalization for, say, post-partum depression in the past.
That should be coupled with text describing any expressed threat to commit acts of violence, murder or suicide. Never mind gun confiscation, they'll steal a gun or use something else....lock them away.
Next it will be the elderly. Already established age limit on the young end and they will say elderly are likely to have poor eyesight, poor coordination, deficient mental abilities, tendency to end their own lives, etc. and so justify no guns after 65 y/o and they will want to link it to withholding social security or some other such scheme. Once you limit various groups you are well on your way to nearly total control and each step will sound very reasonable along the way.