I'm not sure what is the best way to fight it.
The thing about political debates is that the objective isn't to change the mind of the person you're talking to. It's to convince the audience listening/reading along that your side is morally or logically superior. In most cases, the most effective way to do this is convincing them the other side is idiotic or irrational.
In the case of social justice, it's a very hardline issue. Very few people are on the fence about it, they're either deeply for, or deeply against.
This means that convincing anyone requires total destruction of your opponent's argument. But the problem with that is what constitutes domination for one side makes no sense to the other. In the eyes of classical liberalism, social justice is beyond retarded...it is lunacy on a nuclear scale. And conversely, in the eyes of social justice, classical liberalism makes no sense and is evil and stupid. There's no common talking ground. For social justice to make sense to a person requires a fundamentally different view of how reality operates from that of classical liberalism. This makes worthwhile debates nearly impossible. It's like a conversation between a Chinese man and a Swede.
This is a similar parallel to Communism. Communists are notoriously difficult to debate with, not because they are right, but because their arguments make no sense to us, and vice-versa. Really the best way to fight Communism (outside of direct violence, possibly) is to let Communism destroy itself. This is why, while I would still resist Communism in the US, I wouldn't do so at all abroad. The more real-life examples we have of Communism failing like it inevitably does, history itself is simply more and more compelling. It's not fun saying this, but if Communism were never allowed to be tried, and simply stopped again and again, it would merely strengthen the resolve of those who fight for it, and its victory would only be delayed. Think about such a system, how it starved millions in the twentieth century...if people would still fight for it a hundred years from now when there's billions more potential victims.
Social justice has the luxury of being untested, and thus, not yet proven wrong. This leads to my main concern; that the only thing we can do is let social justice destroy itself. Millions would suffer under such a hypocritical, unjust, and ultimately unsustainable system, but is its implementation inevitable? The media and education in the west are soaked in it. It is inescapable, millions of people have fallen for it, or have been scared into compliance. Is there another option?