According to Wikipedia
"Brainwashing, to affect a person's mind by using extreme mental pressure or any other mind-affecting process"
Taking a child and repetitively telling them things about deities and dogma without providing justification (aka teaching to believe based on faith, aka because I said so) and doing so before the age of reason when a child is still vulnerable to believing whatever their parents and other trusted adults is textbook brainwashing.
Yes, religion can brainwash people. Some cults and sects intentionally, on propose do that, usually for some kind of materialistic, economic gain. They are cheating elderly people, scared, lonely and people with mental problems, and also people who seek for hope and companionship. Despaired, depressive people can be easily manipulated by religion, and made to do terrible things in that religion name.
If you look up religion in a dictionary or thesaurus, cult will appear as a synonym. Typically in society we separate these two terms. Religion is positive, while cult is negative and brings to mind evil manipulators such as Charles Manson and Jim Jones. In actuality, many people we consider to be cult members would consider themselves part of a religion. They believe so strongly that they hold to these beliefs taught to them by supposed religious affiliates. It's through this strong faith that people can often be convinced to do terrible things.
As this tragic case has highlighted, religion (like any ideology) can lead its adherents to commit terrible crimes that would be unthinkable to people outside their ideological space. This is not only true in this case but also in the case of Islamic fundamentalist terrorist organisations and other religious institutions throughout the world which practice terrible cruelty.
Only superstitions and false religions do. Religion is supposed to be there for many reasons. Let humans know about their God, why He created them and what are their duties towards Him. Preserve order in the society, through commands that show what are the duties and resposibilities of individulas towards themselves. Clarify the reality behind matters that humans cannot grasp or understand through reasoning. And of course motivate people to preserve their lives.
I think it's wrong to make such a broad statement about religion based on this one incident. I think all people are capable of acting irrationally and religion certainly can affect that. But religion has many positive aspects as well. In this one case, this person committed an unthinkable crime while taking part in their religious activity. But we don't know their history. They may have a long criminal history or a history of violence. Religion did not necessarily have anything to do with it. Most religions promote good qualities in people like kindness, generosity, service, etc. So I don't think it's fair to say that religion brainwashes people based on this case.