As an example I think people from the American political left to somewhere(?) in the middle see it as what it has been introduced as, that being looking past the status quo and instead looking at your own values, i.e. the morality of homelessness and not having a disdain for them but empathy for them instead.
and then on the other side it feels like the people on the American political right see it as what this website describes it as “ A self-righteously moralistic person who behaves as if superior to others.”
I think the divide has originated from taking unlikeable behaviour and labeling that as ‘woke’ (in bad faith of course) and some people have just bonded to that definition so much that they see it as that.
At least that’s what I’ve noticed online over the past few (bonkers) years
The belief consists of two parts:
1. That truth is socially constructed thus when we see bad things, it means society created these bad things.
2. In order to determine what parts of society to cut-out to make society better, so bad things stop happening, use a critical theory to determine who should be removed from society so it can be more equitable (usually the stand in for good.
Woke normally holds that goodness is when results are equal, and if they are not equal, they have license to adjust them to equal (This is the core argument of Marxism, though woke could be said to be identity or social Marxism rather then just the economic Marxism presented, though in practice class identity was present from the start as well and expanded in practice under Mao).
There is no such thing as "society", just relationships between individual people. To get a better "society", you need people to act better. However, all of recorded history suggests that people are pretty universally willing to use other people as tools to benefit themselves. (Obviously not everyone does this all the time or to the same amount.) History also makes it clear that passing laws will not work: despite laws against things that are evenly timelessly non-virtuous, like stealing and murder, do not prevent murder and theft. In fact in Judeo-Christian thinking, to do this requires people receiving a "new heart, a heart of flesh instead of a heart of stone" from God. (I saw "Judeo-" because the passages is from Ezekiel, which is common to both. I do not know if rabbinical thinking agrees, however.) Even if it does not require a divine gift, certainly the problem has proven intractable up to the present time.
"determine who should be removed from society" is just a scary thought. Who gets to determine that? How can we be sure they are right? What prevents them from using this as a tool to eliminate people that are competitors or whom they simply dislike? In fact, this has a name: "to purge". The Soviet Union under Stalin and the Chinese Cultural Revolution were scary times.
It doesn't. Judaism holds that the soul starts out pure, having been made in the image of G-d, and it only becomes impure through wrongdoing. All humans are born with an impulse to do evil, the Yetzer Hara, but we're also created with the power to overcome it. And when we have done evil, we have the ability to atone and return our souls to the pure state they were created in. That happens, for instance, on Yom Kippur.
The context of the verse from Ezekiel is:
> O mortal, when the House of Israel dwelt on their own soil, they defiled it with their ways and their deeds […] So I poured out My wrath on them […] I scattered them among the nations […] But when they came to those nations, they caused My holy name to be profaned, in that it was said of them, “These are GOD’s people, yet they had to leave their land.” […] Say to the House of Israel: Thus said the Sovereign GOD: Not for your sake will I act, O House of Israel, but for My holy name, which you have caused to be profaned among the nations to which you have come. […] I will take you from among the nations and gather you from all the countries, and I will bring you back to your own land. I will sprinkle pure water upon you, and you shall be purified: I will purify you from all your defilement and from all your fetishes. And I will give you a new heart and put a new spirit into you: I will remove the heart of stone from your body and give you a heart of flesh;" https://www.sefaria.org/Ezekiel.36.17-26
Ezekiel lived during the Babylonian exile. At face value, the text is saying that the people of Israel have been exiled because of their sins, but it makes a prophecy that G-d will cause them to stop sinning and return them to their land. That eventually did happen under Cyrus the Great. This is a constant cycle in the bible: When things are good, the Israelites forget G-d's teachings. Then something bad happens, but G-d redeems the Israelites from their suffering, which leads them to follow G-d again. Then thing get good again, and they start to forget G-d once more...
When it says that G-d will give the house of Israel a new heart, it's not (at face value) saying that individual people will literally receive new spirits (or otherwise be metaphysically transformed). Nor is it saying that G-d will literally sprinkle water on them. These are poetic ways of saying that the house of Israel will stop worshiping idols (etc), the same way that happened many times before in the Torah. You can of course add a layer of exegesis and make it about individual believers today instead of the nation of Israel in Babylonia of the 6th-century BCE. That's fine, the rabbinic tradition does that sort of thing all the time too. But at that point you're firmly in Christian territory and not in the space shared between Judaism and Christianity.