The normie right winger sees the failings of the left in terms of their use of racism. They view racism as bad, and the left is bad because their ideology is racially focused, but that it demonizes White people and pushes diversity rather than merit. The latter part is a good position to hold, but it's undermined by the race blindness of normie right wingers. To them, "woke", as it's become attached to the left, is viewed through the above lens. Thus, "woke right" are right wingers who aren't race blind, according to the normies.
The normie right winger sees the failings of the left in terms of their use of racism. They view racism as bad, and the left is bad because their ideology is racially focused, but that it demonizes White people and pushes diversity rather than merit. The latter part is a good position to hold, but it's undermined by the race blindness of normie right wingers. To them, "woke", as it's become attached to the left, is viewed through the above lens. Thus, "woke right" are right wingers who aren't race blind, according to the normies.