Hmmmm. As someone who has tracked BLM pretty closely, and supports it! my impressions are that the vast majority of BLM activists/marchers/supporters are not "Communist" nor even "Marxist." I know the quote you are referencing and I believe the woman who said it almost said it defensively, as I heard it, in response to someone asking her if she had an overaching strategy. ... Nonetheless, the effects of "endless growth capitalism" are not pretty at this point either, and we risk planetary suicide if we continue along our current path. (See my last Medium essay). https://amichen.medium.com/the-climate-crisis-is-time-to-ask-the-deeper-questions-d4de8dcf25e7
Marx had his analysis, which should not be discounted. But overall, we are ALL concerned with authoritarianism of any kind.
There are certainly woke excesses, but IMHO this is almost nothing compared to the rise of neo-fascism and now near constant lying by the Right here. From your comments, I would say that you misunderstand quite a lot about anti-racist education. I highly recommend the books Caste, White Rage and The Sum of Us as a start. This kind of context helps put things in perspective.
It is unfortunate that one woman's comment would paint an entire movement--or even that BLM represents the hundreds and thousands of authors and writers who are POC or who support POC and others who have been oppressed, and doing wonderful work.
All of the authors I have read have great, almost surprising compassion for white people. "Homegrown Hate" is a very important documentary from ABC News about the whitelash to Obama (very real!) and I profile one young BLM activist in my hometown in the essay below, as well as what POC are responding to in terms of Trumpism. If one does not understand the nature and strength of white supremacy in this nation, then "wokeness" might look extreme. It is not. https://amichen.medium.com/waking-up-to-racism-from-your-house-to-thewhite-house-ebe8045933c1