Nobody wakes up one morning an says I'm going to invent some new "woke" policy or cause. "Woke" is just a trope that Republicans are using just like "Critical Race Theory" as a catchall for anything the GOP wants to throw into it to rile up their base.
We can't stop individuals from saying or advocating for stupid things or democrats from coming up with unique new ideas. Republicans and the Fox Propaganda channel will always be able to come up with something they can point at as some new "woke" idea or policy. The fact is most of them never see the light of legislative enactment into law.
The problem for Democrats is messaging. While republicans have no problem endlessly repeating the same attack lines against democrats until they become internalized in the public consciousness, Democratic politicians are loath to go on the offensive. Too many still hold out hope that bipartisanship will come back into style when they should be going for the jugular and calling out blatant lies on a daily basis.
What Democrats need is a new slogan, something like "Democrats; solving problems not inventing them" which they repeat until it's internalized by the public. It would encapsulate the difference between the parties and allow candidates to then dig down into the details like what Build Back Better does for people. Moreover they could then contrast GOP non-issues like Critical Race Theory and Voter Fraud, even "Wokeness", which don't really exist with the problems they are addressing that affect real people. It labels the GOP as wasting their time and ineffective.
In any event, Democratic messaging isn't working right now and it needs a complete overhaul.