In New Jersey, can a parent be denied child custody (or can custody rights be modified, e.g., require a neutral party present during visitations) when one parent has been diagnosed with Generalized Anxiety Disorder? If not, which type of mental illness could have such results?
In a child custody proceeding, in pretty much every U.S. jurisdiction, when the parties don't reach a mutual agreement, a single judge hears evidence and makes a decision designed to be "in the best interests of the child."
There is no real further guidance than that to the judge and pretty much everything about the parents from their personalities to actual diagnosed mental health conditions may be considered insofar as that influences the well being of the child. There are almost no categorial rules (although a number of states have recently passed laws denying rapists parenting rights).