Orthodox Jews don’t looking for converts among non-Jews. They typically turn away three times Gentiles seeking conversion and then only convert them after they have proved themselves.
Now what happens if the convert is sincere but mentally ill?
Different Batei Din (Jewish law courts) and different rabbis have different approaches.
The typical rabbi and the typical Jewish law court are going to be asking themselves if a prospective convert will be more of an asset or a liability to the Jewish people.
In May 2001, when I revealed to the Rabbinical Council of California (RCC) Beit Din that I’d had Chronic Fatigue Syndrome since 1988, Rabbi Avrohom Union raised his hand and said, “That’s a yellow light. It’s not a red light automatically stopping your conversion, it is a caution. Leading a Jewish life is very expensive.”