BS”D
There really is no Neturei Karta anymore.
It was never a movement or Chassidus to begin with; Reb Amram Bloy ZYA was not a rebbe; he davened in Mishkenois HaRoim and their mesivta is named for him. (His daughter, not his niece as I had thought, is married to a well known Chabad posek and his grandchildren are on Chabad shlichus in the Western USA and South America.).
NK was more of an organization that represented the various anti-Zionist groups, provided assistance and even created a parallel economy in Mea Shearim, and organized demonstrations.
The more official remainder of the NK is weak. Those who have taken the name for their own purposes are really just a ragtag band of oisvorfen from every kreiz and yeshiva you can think of (Beck is from Vizhnitz, Weiss is from Chaim Berlin and also tried Satmar and Vizhnitz before getting the boot and joining Beck, Cohen is supposedly a yekke of old British stock, Weberman is from the Malochim of old, Fryman is from YU, the London crew include Polish and Hungarian Chassidim etc).
The only reason they are not in cherem (well, Cohen is in super-cherem in Manchester) is that there is no kehilla in most of the places that they infest to place a binding cherem on them.
Peerim time is the right time to discuss these clowns. In fact Moshe Hirsch of not very blessed memory started off as the Purim Rov in Chaim Berlin years ago. He liked the attention so much that he married into a real NK family, broke with his family, and eventually became the Minister of Jewish Affairs for the PA. He was paid for his work, and his son lives quite well too especially for Mea Shearim.