Terrorism takes place between and across the Islamic sect lines IMO.
Those guys are very fluid between the terrorist organizations. One day they're fighting for one group. The next they are fighting with another.
I don’t believe it’s nearly as fluid as you’re claiming. Iran doesn’t generally support Sunni organizations, and Saudi Arabia doesn’t to my knowledge ever support Shias. These two sects of Islam hate one another at least as much as they hate non-Muslim “infidels.” Furthermore, Iran perceives the Chechens (not incorrectly) as clients of their Saudi enemies. At one point, the Saudis even tried to strike a deal with Putin where they offered to stop aiding Chechen and Dagestani jihadis if Putin stopped aiding Assad in Syria.