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I believe it's referring to self-identification, a process by which the sense of 'I am' is born in relation to our experience, conditioned by, and further conditioning, craving and clinging. It's saying that using a toothbrush and calling it by its conventional designation can be done without clinging to it as 'my' toothbrush and the multiple narratives that this I-making and my-making can create. In essence, "these are the world's designations, the world's expressions, the world's ways of speaking, the world's descriptions, with which the awakened one expresses themselves but without grasping to them" (DN 9).
Realizing the Dao is probably similar to realizing the Dhamma. The only issue is, we don't start out with that knowledge because it's obscured by what Buddhism calls defilements. Being content and accepting things as they are is good from a certain POV, but we wouldn't necessarily want to do that when 'things as they are,' i.e., the contents of our minds, are essentially polluted or coloured by greed, anger, and delusion. If I'm an angry person who beats my spouse, for example, I'd hope I wouldn't just accept that as is but try to uproot the anger that causes such suffering to myself and others. What we should come to accept is the nature of phenomena, its arising and ceasing, its impermanent and selfless nature, etc. And part of the path to that kind of acceptance is the process of uprooting the mental defilements that prevent us from seeing and accepting that reality. When we're tied by self-centredness, we're susceptible to their rule and can't see beyond our sense of self, our likes and dislikes, etc. But when we pierce that veil, we see the Dao, Dhamma, and it all falls away, leaving a bright, clear mind and an acceptance of things as they are. So from that POV, I see Buddhism and Daoism as complimentary and can be likened to different fingers pointing towards the same moon.
I think that Buddhism ultimately encourages us to be non-judgmental rather judgmental in the pursuit of happiness, just as I think Jesus does in Mt 7:1-5. But that doesn't mean we shouldn't use our discernment when trying to achieve that goal in the course of living our lives. The faculty of mindfulness, for example, doesn't judge, but it does make being judicious possible. We certainly don't want to be judgmental in our practice, of ourselves or others, but we do want to make careful observation and judicious decisions. Being judgmental means that we basically make judgments and decisions out of ignorance (i.e., conscious and unconscious biases bubbling up from our likes and dislikes, past conditionings, ect.), whereas being judicious means that we really make an informed decision based upon all the facts and with an eye to what's skillful, i.e., what's conducive to long-term welfare and happiness. To use mindfulness properly, we have to frame our experience within the framework of the four noble truths. Not only do we have to pay attention to our experience, but we also have to use what we learn skillfully, for the purpose of ending suffering.
I was reading a bit from The Brothers Karamazov and watching as the wind wafted through the trees and it got me thinking. Our thoughts and mental states are a lot like leaves sprouting forth and falling from branches of synapses and neurotransmitters. Seemingly countless and often colourful, we think of them as solid, immutable aspects of who we are, arising solely of our own volition and free of any bias. But that's an illusion, really, and we fail to see what fragile and conditioned things they truly are, neglecting to note the rays of sunshine and drops of rain that nourish them, overlooking the cycle of arising and ceasing that the seasons govern, and failing to notice how easily those leaves are swept up and blown about this way and that by the winds of gain and loss, status and disgrace, censure and praise, pleasure and pain, like and dislike. And over the years (especially thanks to Buddhism), I've come to learn that, instead of simply following those leaves in whatever direction they may flit about, it's good to try and stay rooted where we are, in the present moment, regardless of which direction the winds are blowing in order to see things a little more clearly and with a little more equanimity.