Being woke, is being aware of social injustices around you. In a way, is the first step in making any society, or country, a better place for all those who make it up. No action can be made, if one isn't aware of said injustices.
So, being woke should not be considered to pertain to the left or right of the political spectrum. Everyone should be woke to the injustices happening around them, finding a way to correct them, and helping create a more just society. One could contend that a perfect society isn't something we can build, but we all should work to get as close to it as humanly posible.
As such, when anyone tries to use woke as an insult tells me that they are ignorant of what being woke means, or they don't want to be made aware of the injustice around them. Both are just as bad, and it makes it hard to move forward as a society.
While woke is something considered left leaning, it shouldn't be. Being aware of social injustice is something that people in the right and left should be aware of, and to work to fix. There is no reason why any one should argue that fixing systemic injustice is in the best interest of everyone.
Making a society more just for everyone, is something that benefits everyone in that society, directly or indirectly leveling the playing field benefits everyone. Being woke, and pointing to what need to be fixed is something that allows for actions to be taken that benefit everyone in the long run.
Yet, just being woke isn't good enough if it doesn't lead to action for the betterment of society. Pointing to an injustice needs to lead to actions to correct that injustice. We all have benefited from woke, but there is still much work to do and need to remain woke.