The mentally ill come in all the same varieties as people without a mental illness.
You have wicked people who are mentally ill, and their mental illness does not make their evil ways any less wicked.
You have demon possessed people who are mentally ill, who may need both an exorcism and salvation to be cured, and it may well be instant in their cases, but that is certainly not every case.
You have lukewarm Christians with mental illness who use “I’m sick” or “my child is sick” as an excuse to wallow in unrepentant sin. This sort will answer to God on the same terms as lukewarm Christians who find some other excuse for it.
You also have “hot” Christians whose “thorn in the flesh” is a mental illness they’ve prayed for God to remove and gotten the same answer from the Lord that the Apostle Paul received. Jesus Christ has the only cure for what afflicts humanity’s souls, and he has given some instant miracles, but he usually takes our entire lifetimes, that’s true regardless of whether our imperfections and weaknesses come with a medical diagnosis.
And the fact of the matter is, the vast majority of the mentally ill of all stripes and religious or secular persuasions are peaceful, law-abiding citizens and not a threat.
It’s wrong to use mental illness to excuse evil. It’s also wrong to presume everyone who has a mental illness is evil and would be instantly given a sound mind if they only repented of the sins surely causing their problem. Both ideas are destructive lies.