There are certain elements inside the Church which wants to eradicate demonic possession, and thus accomodate modernity. But we should not be looking to "fit in" with the crowd and the superstitions of modernity.
We need a careful evaluation of what demonic possession is, and why secular psychology wants to re-brand it as mental illness, specifically schizophrenia.
The truth is that it is an obscure question that can only truly be answered by people who have throughly studied this subject and have seen many cases of the phenomenon. We cannot leave this question to people who are ignorant. The Church is not a democratic politician who repeats what the crowd wishes in order to get votes. The Church must do what is right and truthful
The truth is that demonic and angelic possession has been subsumed by psychiatry in an effort to securalize society. If you study schizophrenia enough you will understand that what we have always known to be either demnoic or angelic beings have simply been refashioned as audatory and visual hallucinations.
The phenomenon are the same. But since there was an effort to securalize society, doctors, philosophers and politicians needed a way to explain the age old phenomenon in a new and "accepted" way. That's all there is too it.
Try asking any psychiatrist what the voices claim to be. Most of the time they will claim to be what they are. Demons. Why should we as Christians doubt that?