Let's talk about judgment.
For the last few decades, being non-judgmental has been cool. "Oh me? Yeah I don't judge. I love unconditionally" was the sort of high-status signal of the hippies, and more pro-therapy types after them.
This blanket refusal to judge has slowly been changing over time, and for good reason. Unfortunately, we have to judge. The idea that you can just decide to abstain from judgment is a false idol, an idea that seems attractive up front but once you look deeper inside, is completely empty and nonsensical.
One of the ways this non-judgmental mentally has been justified is to refer to Christian scripture, and Jesus' proclamation that we should "judge not, lest we be judged." Ironically, it's usually non-Christians that bring this line up, but that's a whole nother fraught topic...
Anyway, I want to pick apart that verse a bit. It comes from Mark, 7:1-3. The KJV version is:
Judge not, that ye be not judged.
For with what judgment ye judge, ye shall be judged: and with what measure ye mete, it shall be measured to you again.
And why beholdest thou the mote that is in thy brother's eye, but considerest not the beam that is in thine own eye?
So if you just take the first line at face value "Judge not, that ye be not judged," you could make an argument that Christ is saying here - hey, you should never judge anyone! That's not cool!
Luckily, he spells it out very clearly in the next line. "with what measure ye mete, it shall be measured to you again." In other words, the metric you use to judge others will be used to judge you, by God. Regardless of your religious beliefs, this idea definitely represents an interesting twist on morality. It's essentially the golden rule, but with an important variation.
The next line talks about the mote in your brother's eye, and the beam in your own. Here Jesus is saying that you look at a speck of dust in someone else's eye, and make a huge deal out of it, even if you have a gigantic plank sticking out of your own eye. He's emphasizing our penchant to judge others harshly for things that we do ourselves.
He was always very clear that He hated hypocrites.
Now the obvious first-order solution here, which again the sort of new-age hippy movement popularized, is to just throw up your hands and say "I'm not going to judge." Let's get into why that's problematic.
Judgment is Necessary
First off, there is a lot of data in the world. A LOT of data. At a guess, any second you exist in the world you're filtering hundreds of millions (probably more) distinct items of sense data. Particles of light, smells, sounds, physical sensations, your own thoughts, et cetera et cetera. Just to make sense of all of this data, you're constantly judging what information is salient, or relevant, to your life and your decisions.
So the idea that you can just 'not judge' falls flat on it's face. Admittedly though, this idea is a bit abstract. Let's go more into the nitty gritty of what non-judgment looks like in practice.
Would you judge a culture for practicing human sacrifice? Perhaps if the sacrifice is voluntary and religious, you might say "oh well that's fine, that's their right and we should respect their beliefs." Sure, I may not agree but I can understand your reasoning.
What if the sacrifice is non-voluntary, though? What if someone is dragged kicking and screaming to an altar, and has their heart torn out? Even worse, what if this happens to a child? To thousands of children?
These aren't hypotheticals. The sacrifice of innocent children to win the gods' favor was common in the ancient world. It was tension with those Canaanite societies who worshipped Baal and other gods that led to much of the Jewish, and later Christian, moral sensibilities that we operate off as our default today, in the West. (more or less)
Again, judgment is necessary. Now if we go by Jesus' quote in scripture, then this sort of judgment shouldn't be a problem. As long as you aren't planning on sacrificing children any time soon, you don't need to worry about judging others for doing so. In fact, it's probably something seen as a moral imperative by Christ, I would argue.
His point in this verse is not to tell us we should love unconditionally and never judge, but rather to warn us against those petty judgments that are all too common. If you're sitting there and judging your coworker for her choice of dress, or your neighbor for his decision to mow the lawn at 6am, all while refusing to judge horrific practices by foreign cultures, you may need to check your measuring stick.
Ultimately the point I'm trying to make is that if you give up the right to judge, you're abdicating any moral responsibility. You give up all agency, you basically outsource the right to make moral decisions to the people around you. This decision may be correct in some cases, i.e. if someone is severely disabled, or has made extremely poor moral judgments in the past and recognizes the fact.
We must judge, and it's moral and good to do so. The more power and privilege we have, the more important it is for us to develop a refined sense of judgment, so that we don't abuse others unwittingly. However we must always be vigilant to ask ourselves: "am I holding up to this standard I'm using to judge this person?"
For most people who claim to be 'non-judgmental' in the modern age, the refusal to judge is nothing but an act of rank cowardice. It should be treated as such.