That is one of the basic requirements of most religious orders. Yet, what does "good mental health" mean? If a person has a history of depression but has been stable for years... do they have "good mental health "? or should the person aspiring for religious life always be one of those fortunate souls that have never experienced an emotional breakdown?
I don't know the answer to this. I guess it depends on each religious order and on the individual... yet I know that wether the person can or cannot fulfill a vocation, Our Good Lord has a plan of glory for each one of us! Each person, whether sick or healthy, has a mission, a divine task to accomplish!
"He will use you to accomplish great things on the condition that you believe much more in His Love than in your weakness." Mother Teresa