Most of the hesder programs and their students believe the same thing and probably promote disobeying. They are just not as vocal. But by cutting them off, you are cutting off some of the top future leaders of the idf. Why not 'cut politics out of the idf' by refraining from using the idf for political purposes, such as evacuating Jews from their houses and helping the police deliver eviction notices, and instead let them focus on their main goals - "Israel", and "Defense".
Judge orders Jerusalem Gay Pride attacker to undergo psychiatric evaluation (Haaretz)
from the article: Barak orders IDF to cut ties with far-right yeshiva