What I do think it's productive to do is to assess based on evidence the relative weight of people's issues. I think we'd agree that treatment depends on successfully and accurately identifying the problem. A huge part of that is figuring out what order of magnitude of difficulty you've got in front of you.
I'd say that in distinguishing between 'raised with too much self-esteem' and 'chemical imbalance,' the difference in the resulting treatment is so drastic that it may as well be a different diagnosis. Someone in the former category needs to acquire some combination of acceptance, a sense of agency, and goals to strive toward. Someone in the latter needs medication. The former is easier to solve, because the latter in some cases may not be solvable at all. This doesn't mean we should abandon compassion and start yelling at the person, but isn't it a good litmus test? Shouldn't someone who genuinely wants to get better be delighted to hear that their problem wasn't so big after all?
It sounds like you're less against judgment in general and more against lazy, dismissive, heartless judgments. But that's not what I'm advocating at all. I just have sympathy for the war veteran rolling his eyes when he hears a story about someone who got mugged getting PTSD. Of course no one should be mugged, and getting mugged sucks, but oh come on, let the guy roll his eyes.