People say it like it's a damnation of the idea. Things in life are fuzzy, that's why it's literally called a paradox.
The most tolerant people in the world are not going to be ok with a 20 year-old having a sexual relationship with their 12 year old daughter because of the danger involved. That's the paradox of intolerance, that everyone has a limit, and if you have no limit, someone else will pick it for you and cause damage on their terms.
We don't generally tolerate violence in the west. Yes, it's an intolerance, but it's for the greater stability of society.
but I have absolutely seen people use the paradox of tolerance to argue for some shitty opinions, so it must still be dealt with care. You can imagine a KKK member using it to defend their choice of not allowing blacks to be free of lynching.