It’s BY tolerating it (or more specifically, the people who espouse it) that he fights it.

And I think that’s the key difference- tolerating intolerance (the action), vs tolerating the intolerant (the people).

I think we would all (probably including Mr. Davis) agree that the action of intolerance should not be tolerated. For example, if a local movie theater wants to have ‘whites only’ movie nights, that should not be tolerated and in fact we should all aggressively fight back against such things wherever they happen.

But what of the intolerant person? What of the theater owner in the above example? Should we run him out of town? Tar and feather him? Refuse to talk to him?
The KKK folks he encountered are used to intolerance- threats, shouting, protests, etc. They know they’re not popular, but that helps feed the belief that they are right. They’re used to it. They’re NOT used to being welcomed by anti-racists.

And thus Mr. Davis got through to the racist- by tolerating the intolerant, not by tolerating intolerance. It’s a subtle but vital difference.