This is a fair question. First, I'd say that the impression you have of American anti-racism "eating its own tail" is false. Lots of valuable, important work is being done. Unfortunately, the most unreasonable, sensationalist voices get the most air time, which undermines the whole movement. This is what gives this impression and is one aspect of the critique in this piece.

But the other, the question of when the correct approach is understanding and persuasion, I'd say it's at the point where what the other person is doing isn't clearly and rapidly eroding decades of hard fought progress in race relations.

If you think that segregation, especially of children, is a worthwhile strategy for fighting racism, you are more of threat than the actual racists. If you think there is value in questioning the racism of everything from sandwiches to hiking, you are actively undermining the perception of important work. If you argue that every problem in existence is caused by white supremacy, you need a therapist to help you work through you inferiority complex.

There will be disagreements about methodology in any movement. I'm certainly not arrogant enough to claim that I have every single answer. But some things are so obvious that if you can't figure them out for yourself, to stretch the toddler analogy to breaking point, you aren't old enough to get involved.