Consider a group of Neo-Nazis that want to stage a peaceful protest espousing their ideology. They get their permits and set out in a town square, chanting all kinds of anti-Semitic and white power nonsense. The question "are the Neo-Nazis being intolerant?" is a tricky one. On one hand, the answer is a resounding "yes," but on the other, they're the proverbial dog that's all bark and no bite.
Consider some local Jewish group that wants to stage a counter-protest. I'll give you the same question: are the Jewish protesters being intolerant? Again, it's a tricky one: they might argue they're being intolerant of the Neo-Nazis' intolerance (as I'm sure Popper would say).
The Neo-Nazis could, in turn, argue that they aren't being intolerant at all - they're just exercising their First Amendment rights. In fact, it's the Jewish counter-protesters that are the ones being intolerant! So we're just going around in circles debating who's being "intolerant," what "intolerant" means, and what it takes to go from "tolerant" to "intolerant" -- the classic sorites paradox[1]. This is all equivocation.
When we look at simpler tests like Mill's Harm Principle, the problem is simplified! If, the Neo-Nazis aren't harming anyone, they're free to do whatever they please -- as are the Jewish counter-protesters. Harm is a lot easier to wrap one's head around than "tolerance," so that's why I think it's a much more palatable litmus test.
> "Tolerance" is kind of a weasel word anyway, essentially giving carte blanche to the one that invokes the paradox.
How so? Demonstrating that a principle makes for a poor foundation has little bearing on its ultimate validity.