It is really disappointing to see such a disparaging post and subsequent comments on something most of you including the OP do not understand nor care to.
The term "woke" is a political term of African American origin. It refers to an awareness of issues concerning social justice and racial justice. It is derived from the African American Vernacular English expression "stay woke". AAVE being previously known as Ebonics.
If you had the time to make such a disparaging post you also had the time to google the word OP.
"One aforementioned SJW told me that it was racist to dislike the term but was unable to articulate why."
Well fortunately for you I am very happy to articulate the racial aspect to this conversation.
The ridiculing of the term "woke" (and few others by PPs) is part of a much larger debate, there is a LOT of stigma around the use of AAVE which is definitely steeped in classism and racism. A lot of people believe that anyone who uses AAVE is uneducated, ignorant and probably lower class. Stigmatising AAVE is just another way to perpetuate stereotypes about intelligence and wealth. As it is associated with black people and black people have historically been stereotyped as ignorant, uneducated and lower-class, too often many people hear AAVE and think 'haha let's have a good o'l laugh'.
These stereotypes are reinforced by a society which prioritises one set of language or dialect over another. Your lack of understanding regarding AAVE terms does not detract from the fact that it is a real social distinct dialect in English, with its own complexities, a rich history and huge cultural significance with its own grammatical rules. The stance that some kinds of languages are unacceptable and speakers of dialects speak rubbish has real life ramifications.
You are definitely being unreasonable OP.