The important thing is to "know thyself." Ultimately, it requires intrapersonal awareness, which is a trait that many people sadly lack.
I agree that self-awareness is required to avoid projecting, but to be more specific (and, in Jung's words):
Most people confuse “self-knowledge†with knowledge of their conscious ego personalities. Anyone who has any ego-consciousness at all takes it for granted that he knows himself. But the ego knows only its own contents, not the unconscious and its contents. People measure their self knowledge by what the average person in their social environment knows of himself, but not by the real psychic facts which are for the most part hidden from them.
I think it's usually the unconscious that dumps shame into other people through projection (we aren't aware it's happening), so what's required- to
be able to own up to our own unpleasant qualities/shame (or in Jung's terms, 'to bring consciousness to light' and become aware of it)- is enough self compassion to be
able to accept those things about ourselves in the first place.
The thing said at in the second half of the blog post is sorta interesting too. Only I see this happening on a smaller scale too, in interpersonal dynamics between individuals- one person will absorb too much shame between the two of them, and project better qualities into the other person than that other person deserves (e.g. abused partner who stays in a relationship and excuses behavior they shouldn't excuse). This is not a healthy situation of someone becoming self-aware/owning shame that is rightfully theirs (although it can
feel, to them, like it is), this is someone compulsively (unconsciously) absorbing more shame than they should. It's a tendency learned in childhood, when (oversimplified explanation ahead) parents/caregivers are too critical and the only way to 'earn' love is to systematically absorb more than a fair amount of shame.
Another great Jung line that applies here:
Everything that irritates us about others can lead us to an understanding of ourselves.
I'm a die hard believer in that^. (I tried starting
a thread on it before, but it didn't get very far.)