Let me try to steelman it for you: unless we assume God exists in the particular way a given religion says, religion dogma makes a debate around ethical animal slaughtering too inflexible. It is highly unlikely that either kosher or halal rites maximize ethical treatment beyond any chance of improvement (unless you assume divine guidance, obviously), and neither religion is very open to revisit dogma at the pace that ethical understanding of how animals ought to be treated, outside of a religious framework, evolves. Thus, we can consider religious views here as roadblocks.