IMHO, there are exceptions.
In my family, there's is a history of narcissistic personality disorder, borderline personality disorder, Bipolar disorder, and OCD. I have OCD myself. I've never had a problem with psychedelics.
I think there are some mental illnesses that can be brought out by psychoactives(Schizophrenia, psychosis, etc) provided there is a family history of it. But other mental disorder, specifically personality disorder I feel like would take affect no matter what if you have them. Schizophrenia can sort of lie in dormant, but personality disorders are just that; in your personality.
Or at least, that's what I've come to conclude. Just my opinion, though.
One thing, though, is I do think psychedelics aggravate symptoms. I've noticed that when I do acid, my OCD gets a little worse(IE, I become obsessive compulsive over one thing the whole trip. Last time it was my glove lights. I couldn't stop thinking about them and I wore them the whole time and constantly worked on one technique, and things didn't feel right if I wasn't working on that technique. Whenever I closed my eyes, the closed eye visuals usually included my lights. It wasn't unpleasant, and I got very good at that technique. Just had sore fingers the next day, haha)
But I'm still sort of a newbie. =P So this is just my opinion.