Yeah it's a twisted group.. "right wing" no only in the imagination of the FBI and the left
First of all there is an unholy alliance between the white supremacist groups such as the Boogaloo Boys and The Base and the BLM/Antifa combine. Both are anti-Israel. The former has been providing combat arms training to the latter.
Second, it does not surprise me that the Deep State is working with two apparently opposed groups. Similar schemes have occurred before, one being in Northern Ireland, where the KGB had operatives in both the IRA and the Ulsterman. Why, you may ask. Simple. Just to cause strife for what was then the United States greatest ally in NATO.