I was glad to see James Faville link to Tobias Baumann’s post on Longtermism and animal advocacy. I’ll highlight a few quotes relevant to your questions (I especially like the third one):
it stands to reason that good outcomes are only possible if those in power care to a sufficient degree about all sentient beings… What hope is there of a good long-term future (for all sentient beings) as long as people think it is right to disregard the interests of animals (often for frivolous reasons like the taste of meat)? Generally speaking, the values of (powerful) people are arguably the most fundamental determinant of how the future will go, so improving those values is a good lever for shaping the long-term future.
Folks in the comments here have described a number of mechanisms for the immense suffering risks associated with a longterm future that includes animal agriculture, or more generally lacks concern for animals. Those examples make it clear to me that moral progress (with respect to animals, but elsewhere too) is a necessary but not sufficient condition for a positive longterm future. Organizations focused on making moral progress, in this conversation animal advocacy charities, are pretty clearly contributing to the longtermist cause. Of course, that’s not to say animal advocacy charities are the most effective intervention from a longtermist perspective, but right now, my sense is longtermism suffers from a dearth of projects worth funding, and is less concerned with ranking their effectiveness.
a longtermist outlook implies a much stronger focus on achieving long-term social change, and … This entails a focus on the long-term health and stability of the animal advocacy movement.
Meta-charities like ACE, Faunalytics, and Encompass are examples of such organizations, and would probably represent the best fit for a philanthropist influenced by longtermism interested in animal advocacy.
it is crucial that the movement is thoughtful and open-minded… we should also be mindful of how biases might distort our thinking (see e.g. here) and should consider many possible strategies, including unorthodox ones such as the idea of patient philanthropy.
A focus on building epistemic capacity in the animal advocacy movement leads you to similar organizations.
I would sum this article up as “A speciesist society capable of tiling itself across the galaxy is a frightening one we should be actively working to avoid, and this conclusion is robust to a wide variety of future scenarios with respect to AGI, factory farming, wild animal suffering, and alien civilizations.”