My response may seem short and facile, but if an expansion would be useful to you, I would be happy to provide it.
The civilian keeping and bearing of arms is a matter of right, and a constitutionally explicit and fundamental one. The government may not curtail that right without due process. A psychiatric "check"is not due process, though a medical opinion can be an important step on the road to being adjudicated and incompetent.
The other choice is to do nothing. Would you be happy for a person that had accessed to be a risk of harming himself or others. Buying firearms and living beside you and your family.