The question asks in a nutshell, "Why are Christians so hostile against those with mental illnesses?"  The most simple answer might be fear.  After all, we're almost always hostile to that we fear.  Why fear?  Chances are, because a lot of us don't understand mental illness.   Lack of knowledge = fear = hostility.

Another questions asks, "What is the cause of mental illness?"  Some say it's demonic possession, while others say it's chemical imbalances in the brain.  The answer?  Very likely both are the causes.

Let's take a look at least two disorders that are blamed on demonic possession/oppression;  hearing voices, and self injury.

Hearing voices - Often hearing hostile voices either inside the mind or outside the mind.  First, the hearing of voices isn't limited to just schizophrenics.  With that out of the way,  those who support the demonic possession cause might be on to something.  First of all, the voices are almost always extremely hostile and damaging.  These are voices that tell people that they're useless, pieces of crap, that nobody loves them, and that they should die. 

Demons are masters of discord, it could be said that they're miserable, and want humanity to be miserable as well; or it could be said that demons derive from their happiness and pleasure from causing misery.

There's also the voices that tell people to do certain things.  We all know about this; those people who kill ,maybe once, but often more, and because a "higher power" told them to kill.  Now, more often than not, those who blame their murders on God or the Devil or whatever are not always telling the truth.  Those that are sincere in claiming that God or the devil is responsible are deceived in that it's always a demon or even Satan causing this.  The Godhead would never command someone to kill another person, not in this age, not when we have the justice system (which is flawed) which has the death penalty.  (The Godhead will use all things for their purpose.)

In the case of science, the answer seems to be that it's a chemical imbalance in the brain.  However, often these voices can say things not known by the hearer, so a simple chemical imbalance seems unlikely.

If hearing voices is demonic possession, does this mean that Christians should go around tossing holy water at these people, screaming at them like raving lunatics?  God forbid, because that would make most look like lunatics themselves, and the demons may cause their host to attack them. 

Until the person receives knowledge that they're being possessed/oppressed, then the best course of action would be treatment.  Note that this is not a cure, or even healing, but better for the effects to be lessened until the full healing from the Godhead can occur, than to remain completely miserable.

The next issue is one that might hit a little close to home for some people, and that's self injury.  Self injury is defined as the deliberate harming of one self, usually by cutting.  There are two types of self injurers; those who do it, because they think it's cool, and want attention; and those who self injure, because they feel they have no other emotional outlet.  This group will actually try to hide the evidence of their self injury.

The Bible tells the story of a demon possessed exiled man who would cut himself on the rocks.  If the man was trying to "cut" the demon out of him, we don't know, but it's only after Jesus casts the demon(s) out that the man stops injuring himself. 

In today's society, those with S.I.D. are not exiled physically from people, but for a while they were known as the untouchables.  It should be known that for many self injurers they view cutting as a last resort.  Most of them come from abusive homes, and these are the ones that are told over and over again that their emotions are invalid.  That they need to shut up, and that showing any sort of sadness, or anger is nothing more than feeling sorry for themselves.  They are not allowed to cried, yell, or anything of the sort.

People like this are aware of their own emotional state.  They know that they're in pain, but are now afraid to display it for fear of being abused.  Therefore they see only two options; two emotional outlets; to either destroy what is around them, or to turn their anger towards themselves and to harm themselves.  Most self injurers don't want to intentionally hurt anyone else so they instead harm themselves.

Demon possession?

Hard to say, because while that could be the case, S.I.D. is often caused by outside forces, or feeling that having any kind of emotion is an evil sin.

People with  this disorder need to be taught that having feelings is valid, and that even anger and sadness are valid; then they need to be taught how to display those emotions in a non-destructive way, and how to get away from those that might hinder them.

There are of course several more mental illnesses, which I won't go into here.  There is another one that I will go into, and that's depression.  Is this the result of demon possession?   Can it really be when people like Moses, Elijah, King Solomon, and Jeremiah suffered with bouts of depression?   Depression may not be demon possession, so much as it is the result of fallen man.  Specifically fallen man realizing that everything is in vain, especially that done by man.

While a few mental illnesses are the result of demonic possession/oppression, they should not be blamed for all mental ailments.  Furthermore, those who suffer with these afflictions must be shown love.  Not the cotton candy type of love either, but real love.  And no, beating a person's affliction out of them is NOT love.