This is not always true among social movements, but it seems to usually be partly true. Hitler was a reaction to Lenin. But his reaction borrowed from that which it reacted against -- the notion of terror, a powerful government, scapegoating. The Crusades also borrowed from Islamic jihad, even as they fought it, as Tillich noted.
Given CRT, then, one can expect a social reaction that will be tempted to borrow elements from, say, the 2020 racist anti-racist riots. One might argue that 1/6 did just that. Which is not to say reactions are never justified, but only to recognize the danger of becoming what we oppose. (What Girard calls "mimetic violence.")
Or to put it another way, among those reacting against an evil (like Wokeism), one can expect the opposition to belong to a spectrum of positions and characters. Billy Graham and Pope John Paul II were anti-communist. So was Ayn Rand.
To be effective, one needs allies: a "big tent." The usual habit, once the war ends, is to split into new factions and fight over the spoils. But in the meanwhile, one circles wagons, and overlooks the faults of one's allies, especially in the heat of the battle.
These are among the natural dynamics of a resistance movement. Perhaps they are unavoidable. When the Borg invades, communists and conservatives will rightly fight side-by-side. And one can hope to win allies more deeply during that fight.
But to do that, one must remain faithful to one's deepest values, to the Gospel that judges us all. So even if one joins an army, one must remain critical of it, and never join it in doing wrong.
Who said life was supposed to be easy?
So fight the Woke Revolution and other social evils with vigor, "taking heed, lest you fall."