The way halal slaughter is done in NZ allows for reversibly stunning the animal before death, so there is not much difference between it and regular slaughter. The animal could conceivably wake up (an important point to religious folks), but the time between stunning and slaughter is so short that the animal will not wake up (an important point for welfare reasons).
Because the Middle East is a recipient of a fair amount of lamb, that's just the way it's done. The countries that NZ exports to determine much of what goes on in NZ freezing works -- this is true whether the meat goes to the US, the EU, China or the Middle East.
From what I've seen, the ritual slaughterer is a Muslim, is situated so that the animal is facing Mecca and is praying as the knife slits the animal's throat. It's a much better death than I thought it might be. What I saw was on a high-volume sheep processing line on the South Island.
I don't know if you think people would object on humane grounds or due to anti-Muslim bias. On humane grounds, though, I don't think people have a case.