' ...... the children of Moon, Night, Lilith and Faerie, all are souled. It seems that you rules as to what does and does not constitute a human being are stricter than our own. Do you intend to challange Heaven, like that other Morning Star ..... ' - Raziel in City of Glass. Surely Raziel's own words should carry a lot of weight with the Clave, if Clary were to testify as to what she heard. It would be a strong argument against the Cohort.
This is an interesting question. Clary very likely already has made this testimony. What Raziel said to Valentine wasn’t a surprise. Shadowhunters have known for a long time that Downworlders have souls, or at least that there is no good reason to believe that they don’t. But there are always people who believe that they want to believe, and people who will interpret what they hear in a way that is consistent their preexisting beliefs.
None of the discussion of restricting Downworlder rights in Lord of Shadows touches on whether or not they have souls. Shadowhunters are perfectly capable of discriminating against their own. The root of the Cohort’s hatred of Downworlders is xenophobic fear, not logic.
Essentially you’re asking the question “Why, if God said ‘Thou Shalt Not Kill,’ do we still have war?” I wish I could answer. But as a novelist, I tend to be more focused on exploring questions than on answering them. : )