From Wikipedia:
Woke is an English adjective meaning "alert to racial prejudice and discrimination" that originated in African-American Vernacular English (AAVE). Beginning in the 2010s, it came to encompass a broader awareness of social inequalities such as sexism, and has also been used as shorthand for American Left ideas involving identity politics and social justice, such as the notion of white privilege and slavery reparations for African Americans.
The phrase stay woke had emerged in AAVE by the 1930s, in some contexts referring to an awareness of the social and political issues affecting African Americans. The phrase was uttered in a recording by Lead Belly and later by Erykah Badu. Following the shooting of Michael Brown in Ferguson, Missouri in 2014, the phrase was popularised by Black Lives Matter (BLM) activists seeking to raise awareness about police shootings of African Americans. After seeing use on Black Twitter, the term woke became an Internet meme and was increasingly used by white people, often to signal their support for BLM, which some commentators have criticised as cultural appropriation. Mainly associated with the millennial generation, the term spread internationally and was added to the Oxford English Dictionary in 2017.
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Being woke means that serving watermelon and fried chicken and collard greens on Juneteenth is an insult. (looking at the Children's Museum of Indianapolis)
Being woke means understanding why "Circling the wagons" when around Native Americans would be a terrible insult.
Being woke means understanding calling something a "cakewalk" brings up slave-history in the south where African Americans were forced to walk around and whoever "won" got a cake.
Being woke means understanding the child's song "knick knack paddywhack, give a dog a bone" is referring to watching Irish die in the Famine, and would rather give a dog the cast-offs rather than the Irish.
Being woke means understanding "Hip hip hurray" is a deeply antisemitic slur regarding the Hep-Hep riots in 19c Germany where many thousands of recently-freed Jews were lynched.
Remembering and understanding these historically terrible sayings are bad to you and your fellow anti-woke people. Naturally, these sayings require a bit of maturity, intelligence, and understanding to see why these phrases are terrible - and not everyone practices in using those faculties on a regular basis. It all comes down to the same core beliefs: "my race/sex/demographic is superior, and theirs is subservient to mine."
There are other terms for being "anti-woke". They usually wore white pointy hats, burned crosses in "undesirables" yards, and arranged public executions via tree and rope.