The point of cause neutrality is to be indifferent between causes based on any criteria except how much good you can do by focussing on that cause area. The advantage of being cause-neutral is, instead of choosing what to do based on how much you like the cause or any other reason, you are choosing based on how much of a difference you can make.
People who exclude causes because they think there is less room for doing good are cause-neutral, people who exclude causes based on other reasons are not cause neutral. As the reason you are exclusively focussed on animals is because that's where you think you can help the most, you seem cause-neutral. Cause-neutral people can come to different conclusions as to which causes to support, what makes them alike is how they decide on the cause(s) they currently focus on.
GWWC is cause-neutral if it would be willing to no longer focus on poverty and global health if it was convinced that by focussing on other cause areas they could do more good. It is my understanding that the only reason they are committed to poverty and global health is because this cause area is where they believe they can do the most good. If they were to receive evidence that contradicted that, they would no longer focus on poverty and global health. The reason they are focussed on this cause is because they care only about the difference they can make in their cause selection. The reason they focus on this cause is because they are cause-neutral.
I really liked this post. Cause-neutrality is one thing, scope of one's moral system is another.
It makes sense that if you consider people alive today as more morally significant than future people or non-human animals that global health is a cause-neutral thing to recommend. It does save the most current lives and also likely reduces the most suffering of currently living people.
I think most people think people are equal, but future people and non-human animals are more controversial topics. Because they are more controversial and more complicated topics, you have to question your moral system in order to include them. Being cause-neutral based on what people already value is one thing, getting them to think why they value what they value is a whole different ball-game. It doesn't seem unreasonable to me for an organization like GWWC to focus on being cause-neutral based on the scope of most people's moral system and other organizations look at where you should donate if you consider future people and non-human animals significant.