The עיקרי האמונה of a קנאי
There are a number of עיקרי האמונה
1. It is assur to participate in elections
2. It is assur to take government money for education
3. It is assur to speak in Hebrew. This rule is not absolute.
4. The only hashgacha that is acceptable is Badatz Edah Hachareidis
Each group of Kannaim adds their own issurim as well.
Just like there is a Shulchan Aruch for halacha there is a Shulchan Aruch for קנאות, the sefer ויואל משה written by the Satmar Rebbe is the Shulchan Aruch for קנאות. What he assurs is assur what he doesn't assur is mutar. Here are some examples:
1. Satmar does not get involved with demonstrations against chilul shabbos
2. It is assur to go to go the Holy places (e.g. the kotel) that were captured in 1967
3. They do take money from Bituach Leumi
Satmar is very much inward focused.
Toldos Aharon is more extreme then Satmar. They don't take money from Bituach leumi, they won't work for a government company (e.g. Egged). They don't belong to a Kupat Cholim. Because of this it is a very poor community where there are very few opportunities for jobs. Most people work in מלאכת הקדש. Very few people can sit and learn all day because of the financial hardship.
The following typifies Toldos Aharon. In the introduction to the sefer שומרי אמונים the Rebbe writes "The opposition to the ציונים needs to be so great that if the government made a law to put on tefillin every day, you shouldn't put on Tefillin"
The Neturei Karta start where Toldos Aharon ends. The big difference is in there attitude towards the Arabs. The Neturei Karta meet with Arabs etc.
Who is a קנאי? Someone for whom כבוד שמים burns for them, it is the only thing for them.