This isn't just any extremist cult. This is the Death Watch, to which Bo Katan once belonged. In fact, she was a leader of the Night Owls and served Pere Vizsla.
All this is referenced when Paz Vizsla called her "Night Owl" when they arrived at the Watch's cavern. He didn't know it was Bo Katan, but he knew from her helmet she had been one of the Night Owls. One reason Vizsla seems unhappy that they are welcomed is that he at least partially blames Bo Katan for the death of Pre Vizsla at Darth Maul's hand since she was part of Pre Vizsla's group that joined with Maul to take over Mandalore from Satine.

At any rate, Bo Katan knows exactly who this group is since she was once one of them. How she feels about being reunited with them is what's at question, but as stated in an earlier post, it seems like episode 2 was about her redemption. She now has proof Mandalore is not poisoned and has every reason to want to reclaim her home world. Likely she will become the leader of the Watch through some circumstance that will put the Darksabre back in her hand. Since she is royalty and a redeemed member of the Watch, there is little reason for the group not to take her side if and when she regains the Darksabre.