and psychiatric tests

I can’t see any way that this could possibly go wrong, not ever. /s

Let’s look at this on multiple fronts.

First, who is going to pay for that? Are you going to require people to pay for the ability to exercise their constitutionally-guaranteed rights? What other rights would you say that people should need to pay for in order to be able to use them?

Second, what criteria would you use to determine if someone is “fit”? A criminal background check is objective; wither you’ve been convicted of a crime or you haven’t. A psychiatric test is about an indeterminate future, an even that hasn’t happened yet. How are you going to guarantee that only people who will create a crime are being prevented from having rights, and not any other people?

Third, how do you distinguish between a protected political opinion (“the bourgeoisie need to be violently overthrown through force of arms by the proletariat”) and beliefs that have no rational basis in protected political speech (“pedophile Jews are killing people with space lasers, therefore I need to murder everyone at Lollapalooza”)? Given that involuntary commitment is already a disqualifying factor for owning a firearm, how is your proposal meaningfully different unless you are arguing that many people should not be permitted to exercise their protected rights because they might act in a criminal way at some indeterminate point in the future?