Really meaningless study. The question is, who created the woke (far left) agenda? It is the college educated who manufacture the ideologies for both sides. So it comes from higher ed, there's really no denying that fact. Once the ideas are created they are then spread via media (MSM and Twitter) and schools of education. In the public sphere, they are taken up by all who are inclined to believe the message. It's not like college is a barrier to being exposed to woke messaging.
To test this hypothesis, what matters is whether or not the people who DO actually insist on saying "Latinx" instead of "Latino" and "Pregnant people" rather than "Pregnant women" are overeducated. I suspect many of them probably have PhDs.
Most of the criticism about wokeness is directed towards the social science and humanities departments. I'd suspect that STEM graduates tend to be less woke than the average population, but they don't have the same cultural influence.
At the risk of being too overly politically for HN, I posit that wokeness is a distraction that is amplified by people in power (mostly on the right) to try to create artificial class conflict (me vs the woke “elites”). This distracts from the real class conflicts in our society. Highly recommend the recent Citations Needed podcast about this (two part on the GOPs “Rightwing Populism” Rebrand).