The woke movement is used to undermine inequality
Much like political correctness before it, the term "woke" is just another effigy in the culture wars. Its use by the right is an attack on the left's broader ideology of social justice and fighting inequity. Despite acting as if their criticisms were attacking the means by which social equity is achieved, they are actually undermining the road to equality. Through their criticisms of outliers and the anomalous acts of individuals, they miss the larger purpose of the movement: to quash injustice. Their misrepresentation of many of the movement's views acts as a barrier to achieving equity. Woke culture has entered the mainstream of political discourse. Blindly criticizing it only serves as a barrier to the only viable social justice movement aiming to achieve better outcomes for oppressed groups. If we look to the past, every noble cause had opponents who criticized the means and methods of achieving a more just society, and this is no different. No cause passes every purity test, but a myopic focus on its flaws while ignoring its potential benefits, is irresponsible. 
Every movement may have its flaws, but how would they be corrected without criticism? For the right, wokeness has so many glaring faults in how what and how it seeks justice that it would irresponsible not to speak up. Even worse, its just political correctness with a new coat of paint and more problems. Wokeness focuses on too many fringe issues that the general public does not care about, so to make the rest of society bend to its will is foolish. There are other more important problems to face, like the economy, censoring of free speech, and big government that needs to be addressed. Solving those issues will make society fairer.
[P1] The right's use of "woke" is in an effort to undermine the legitimacy of social justice causes and the left as a whole. [P2] Disproportional focus on the flaws of a social justice movement distract from its primary goals.
Rejecting the premises
[Rejecting P1] The right uses woke as a reflection of the movement's actions and rhetoric. The definition has not changed. [Rejecting P2] Without criticism, the movement would not be able to correct its excesses.