First of all, it’s Neturei Karta.
Second:
There are two groups that call themselves “Neturei Karta” (actually, more). They can be divided in two groups, roughly.
About 80-90% belong to the ‘moderate’ wing which holds pretty strong demonstrations, burn Israeli flags, and the like. But they DO NOT cooperate with the Arabs in ANY WAY. They strongly oppose using the internet for anything as well.
Only 10-20% belong to the ‘extremist’ wing which go to Ramallah, Gaza and Teheran and love Ahmedinejad, the guys who went to Arafat’s funeral.
Read the Wikipedia article for more and for a pashkevil from the moderate group against the extremists (I wrote that section).