Now, onwards to the fight for animal rights, the saving of children in Africa, the application of utilitarian principles to our charity work, and all the rest.

Global poverty don't generally state or imply utilitarianism or similar views, though x-riskers do (at least those who value non-existent people). I personally favour global poverty charities, and am quite tentative in my attitudes to many mainstream ethical theories, and don't think being more so would affect my donations (though being less so might).

But the other issue is that it seems like you yourselves haven't given much thought to those positions. How do you know they're right, those philosophical and moral ideas?

The degree of thought varies a lot, sure. I agree that people should spend more time on them when they're action relevant, as they are for people who'd act to prevent x-risk if they accepted them.

In most EA writings I've seen, they are breezily assumed.

Breezy assumption isn't optimal, but detailed writing about ethical theory isn't either.