Friends of Red Jenny -- basically for hunting down everyone from corrupt authorities to nasty gang-men.
Also for the hypocrisy in being as bad/worse than the very people she wages war on.
Nah, I reckon that Sera's own personal hatred of nobles is what influenced what jobs she takes and the direction of her own cell of the FoRJ, rather than something that the group as a whole tend to endorse, since there were a ton of corrupt jerkass nobles living in Kirkwall and the resident Jenny seemed more interested in getting Hawke to take out the street gangs?
(Although she could have been shanking nobles on the side and felt Hawke was too high profile to use for this, or felt no reason to get involved because the numerous merc companies in Kirkwall like the Red Iron were already being hired by nobles to off their rivals?)
But Hawke probably would suit the FoRJ if they were to join anything, since they've already been involved in some capacity in it's operations in Kirkwall and furthermore, has their cousin Charade now operating the Tantervale chapter?