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I just got to put my "nickel" in on this topic - for two reasons.

First Reason #1:
I have past experience with respect to people that have many psychiatric issues, i.e. those who are mentally ill.

The behaviour of an individual is never the same as another; so don't assume typical behavioural responses.
Also, unless that person lives in a stable and consistent environment, their behaviour may not be the same from one day to the next.
So, in a SHTF scenario, or come Bug-Out time, expect anyone in your immediate group with "issues" who is not trained to start losing it.
Keep a keen eye.
If that person has long been "stable" and is constantly training, then they should be good.

NOTE: Yes, medication is "usually" important,
but it is the counselling and support mechanisms, i.e. family and friends, that is EXTREMELY important to maintain moderated behaviours.
Get the wrong mix and you get the wrong results.

NOTE: for those with EXTREME delusional behavioural issues, medication is super important.
There are people who go on to lead quite normal lives if properly medicated at the right levels.
If you know such people, and they are willing to listen about "prepping,"
have them start stock-piling their medications - just don't skip taking any.

Singlecell;
"If anything a SHTF scenario would invigorate everyone who is depressed. BEHOLD! Here is now a real reason to get up in the morning! As for the rest of the mentally ill...."
... NOT bloody likely.

The only way to get a truly depressed person "moving" to do something is to be the "Drill Sargent" to their "Private" ordering them to tasks.
I have had to do it.
At least once they learn a routine, they're good but need the support framework of friends or a group.

I don't like to say this next, but I do.
If I had to choose between categories of those who are ill, I'd choose in this order:
Bipolars, Depressives, schizophrenics (sic) .
Yes, "sic" can be compassionate, but they can be the most unpredictable if not taking medication - even sometimes when medicated.
Those with Bipolar are generally the best at task performance & goal achievement, and need little guidance; in fact they can make the best leaders.
Depressives, as noted before, generally need guidance in task performance, but if given a regular routine will perform quite well.

Reason #2:
Be super aware of "FRINGE" groups and cults.

These are the "nut"-cases to really shy away from, especially in remote areas.
A lot of them are already well established remote areas, and in beautiful, pristine valleys and mountainous areas.

I'm not just talking about "religious" / church affiliations, but other organized or self-named groups.

Personally, I'd be ultra-careful with the anarchist groups out there.
One group that is getting a lot of press right now is "Freeman" or "Freeman-of-the-land."
http://www.cbc.ca/news/canada/edmonton/freemen-take-over-grande-prairie-cabin-trappers-say-1.1912428

Edit: the story on these "Freeman-on-the-land" is now getting more coverage, in local papers, e.g. Edmonton Journal and Sun.
CBC has also updated the story as well. Lots of comments on the CBC site about it. NOTE: I appear as Op-Ed in the comments.

(there was also the case of the Freeman "embassy" set up in a rental home in Calgary recently.)

She's brave....but stupid....

Not only did she pick a fight with a bunch of linesmen...she picked a fight with a bunch of Australian Linesmen? lol. Interesting to see what happens.