Here's some food for thought. Lets say you live with your kid who is a drug addict. Should you be required by law to lock your guns away from him or her even while you are in the house?
You could extrapolate this line of thinking to living with mentally ill, former felons, registered sex offenders, etc.
From a liability perspective, I would think the answer comes down to would it be reasonable to lock up the guns to prohibit access to such individuals? Depending on the cirumstances, it may or may not be. That doesn't answer your question as to whether the state should require the particular activity (I say they should not).