It seems my general experience has been different to others posting in this thread.
Things can vary greatly from one church to another, and within churches from one person to another. I'm a bit choosy nowadays about who I'll talk to at our church to "destress/debrief" (it's a bit TMI for some people, and too much to explain with some others), but I know there are some who genuinely understand, often because they or a family member has experienced serious mental illness.
I know several members who have mental illnesses of the long term sort, and others have experienced shorter term problems. One had to be admitted to a psych. clinic a while ago, when despite medication, her usually well-controlled condition went pear shaped. As far as I know, no-one harassed her about it, she seemed comfortable enough explaining why she'd been away for a bit, and I simply checked up on how she was now that the bad episode had passed.
I know I'm struggling with depression that's creeping up on me more over time, and it's massively encouraging to me that God knows it all and I don't have to explain anything to him. I can pray without having to run through all the complex background stuff first. There is an awful and damaging myth running around in Christian circles that being a Christian means being happy-happy all the time. That's not the example Jesus gave. He grieved deeply over the deaths of people he was close to (John the Baptist and Lazarus) and over people who were unreachable (mourning over Jerusalem, and being sad at the rich young man who walked away from his invitation to join them). The Psalms have some amazing praise songs, and also some crushingly deep laments. I only have to read those to know that I'm not alone, and not unnoticed.
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13 YARN