2. It is the opinion on the behavior as being good or bad that is subjective
Now, you can argue about what outcomes are good or bad, but that's a different issue.
In any event, these things aren't as different from other areas of medicine as you think.
For example, you're full of microbes at the moment. Some of them might make you feel a little off sometimes, some of them might make you incapacitated, and sometimes it might depend. The decision to seek care and/or intervene is a subjective decision, based on your subjective appraisal of how you're doing, and a provider's appraisal. Does that mean that infectious disease medicine is subjective?
Subjectivity enters into all medicine at some point, via ethical decisions about whether and/or how to intervene. Because ethics involves some level of subjectivity, it's unavoidable.
Nobody is locked up simply because they are diagnosed with a "mental illness" which is what you apparently want people to believe - you edited your parent comment, where you claimed that a diagnosis of schizophrenia was grounds for 5150. It's not.
2) No, there is no opinion about "good or bad" in diagnosing mental illness. The almost ubiquitous criteria is significant impairment - which almost always is an impairment the patient themselves identify (not someone else) and are seeking help for.
Please let's you and I spend some time together in the emergency department. Last week we had a patient there who'd been brought in against his will by the police, and who claimed that the chip implanted in their brain was telling him to remove his eyes and everyone else's eyes with the spoon he carried in his back pocket.
He'd already removed his left eye, with the spoon he carried in his back pocket.
Please tell us your plan. I'm sorry that I can't find a throat swab to assist us.
Or perhaps we could have lunch down at the dementia care facility, where the neurologists would love you to tell them they're not legitimate medical doctors because they don't have a throat swab for dementia yet, and because they "lock up" dementia sufferers with a few signatures at the request of dementia-sufferer families so they, the dementia patients, don't walk onto the freeway. They actually lock people up protectively before "the crime" of actually walking onto the freeway.
Imagine that.
Aren't a few signatures (even sans diagnosis) all that's needed to place children in what in effect is protective custody?
2. A behavioral record is no less objective than a biological one. Facebook and Google make a ton of money this way; if you want to offer a biological alternative, no one is stopping you.