The Paradox of tolerance almost never means what the person invoking it as a rebuttal to free speech thinks it means. It's not some moral axiom that demands action to shut down problematic speech whenever it happens. It's a concept that has varied views on to what extent should tolerance of intolerance be extended and to what response is appropriate when it extends beyonds that threshold.

The most frequently quoted text I've seen is Karl Popper's writing, where he states that we must reserve the right to suppress intolerant philosophies, not that we should always suppress them.

Now, some people might have the opinion that we should be completely intolerant to intolerance and that might be a defendable position in its own right, but the paradox of tolerance is not intrinsically condoning that sort of response.