Are they genuinely trying to stifle education, or is it all just racist bullshit?
That's the fun part: stifling education is the racist bullshit.
They've been anti-education since desegregation. Back in the '60s the Religious Right, particularly Oral Roberts, Jerry Falwell, and the people in that orbit, tried really hard to go through the courts and use their freedom of religion under the First Amendment to keep black people out of their church-based schools. Obviously they lost, but they have never forgotten how the mean ol' federal government defiled their perfect little angels by forcing them sit next to some filthy negro while they learn their multiplication tables or whatever. Ever since then they've made it their mission to destroy public education.
By the 1980s that Evangelical movement had become fully ingrained into the Republican party, and that drive to destroy public education came with it. It's what's behind the push for charter schools. It's what's behind the push for private school vouchers. It's what's behind Evangelicals astroturfing school board meetings, and sometimes taking over the school board itself. It's a big part of why public schools (inner city public schools in particular) have been chronically underfunded for longer than I've been alive. It was racism the whole time.
But yeah, whenever I hear a conservative use the word "woke," I've found you can pretty much always mentally transpose "woke" with "ni--er stuff" (or "fa--ot stuff," depending on the context) and whatever they're trying to say suddenly makes a lot more sense.