Unfortunately, I don't think what you are describing ever existed. Every "get-together-group" I can think of has some kind of common interest, even if its something as simple as drinking coffee or reading books. I think your attachment to the church has a lot more to do with your emotions than thinking rationally. The way I see it, the cat is out of the bag with regards to organized religion. It is well known that there have been many corrupt religious organizations and heinous acts committed in the name of religion. To make the argument "The economy was shut down last year and there is a massive issue in our society with depression and loneliness as a result, but it's what those liberals deserve for leaving the church!" is asinine.
>Church is the only place they're going to be exposed to others that may share absolutely no interests with them
Are the bible, history of the church, the nature of reality, and developing a community not shared interests? Also, was the point of the article to only talk to people without shared interests? Isn't one of the first things you do when you get to know someone is try to find a common interest?