Hellboy is of the opinion that the safety of humans (or deer people, in this case...) are always more important than supernatural beings. Since the gods of this world have proven to be too meddlesome with the mortals who live here, especially to the point of genocide and overprotectiveness (the Nalawi falling into anarchy without their Gifts), he agrees they need to be destroyed. He's not motivated by revenge or justice, so he's less aggressive about his opinions than others -- however, with the news that this is the only way for the planet to continue, he's much more willing to argue the point.

Rick honestly doesn't care and just wants off the planet. Whatever will get them somewhere else the quickest ¯\_(ツ)_/¯