"Woke" is only seen as an insult now because the cause is so riddled with issues. Criticism is easy when wokeness engages in so may excesses that are not only unpopular with most people, but also not practical.
It's hypocritical to accuse all critics of being white conservatives when polls show that those most concerned with social justice are white liberals.
If wokeness did aim to correct oppression, then why is the liberal elite the most opinionated about it?
Lastly, conservatives are just as concerned about justice and equality. However, the right has a different idea of how to achieve it. Through economic opportunity and reducing government overreach, everyone will have more freedom to live the lives they want. Plus, radical change never has the intended outcomes, so a conservative approach to these issues is necessary to see actual changes.