You're right about the treatments for chickens and maybe some cows, but there is a difference between killing a cow for the meat, and using its milk; killing a chicken for the meat, or using its eggs.
Both for the chickens and the cows, there are humane/"animate" ways of getting the job done, without harming the animals. This doesn't work if you're after their meat. Both chickens and cows do want to get rid of their natural productions. And there are ways of getting to it, in which they are not abused. This should be promoted. Of course, they don't want to be killed in the process, nor afterwards. That should be stressed as well.
For sure, calling on celebreties to defend a cause is mostly an orchestrated thing. I think you're right to point that out.
However, the question is whether it is a just cause. I guess it is, and even if Moz wears leather, it shouldn't detract him from supporting the same cause.
It's a good thing to set the standard high, and subsequently try to attain it. It would be wrong to give up pursuing it at the slightest inconsistency. Things can be improved. I guess that's what life is for.

Bottomline: I don't intend to defend Morrissey - he should do that himself, nor to excuse him (idem). I just want to say that I'd rather see him promoting this kind of organization, than promoting toothpaste on national TV.