Maybe the simplest way to explain why the Neturei Karta are wrong is to say:
They do not know when to stop.
Maybe they had a legitimate argument [shita] 150 years ago, or 120 years ago, or even 100 years ago, but they lost that debate 75 years ago, and they are the only people who do not know that.
I once learned that if a Jew speaks Lashon HaRa, and the person listening is not Jewish, then the speaker is guilty of both Lashon HaRa AND CHILLUL HASHEM.
(I do not remember the exact source for this, maybe someone reading this can give us the exact source.)
Since the Neturei Karta repeatedly speak negatively about Jews, and millions of non-Jewish people listen to them, they are guilty of both Lashon HaRa AND CHILLUL HASHEM.
The Neturei Karta repeatedly show millions of non-Jewish people that Jews are disunited and hate each other, which is also a Chillul HaShem.