Effective altruism is now spending a great deal of time on improving prospects for the future. This is chiefly by avoiding extinction risks, but there are other strategies as well, e.g. moral circle expansion. In any case changing institutions looks like a promising strategy, either to spread moral consideration for animals and future people. What are the longest-lasting institutions in the world? Certainly high among them is religion. For this reason, it seems to me that influencing religion, particularly old religions with a tendency to grow, is a highly-neglected strategy for improving the world.
I've seen posts in effective altruism (e.g. this one) about outreach to religious groups, but I always saw them as a sort of diversity and inclusivity message: to grow a movement, you need to welcome all sorts of people. It's important to welcome and include people, of course, but this seems to be dramatically underselling the importance of religion. The Catholic Church is around 2000 years old, and while it and its religion have changed, many of its core themes continue to influence and frame society. Progress might be slow for a movement that smacks of secularism, but as much as religion is lasting, it does have a capacity to mutate under different influences. If you are interested in social change not for its rapidity but for its duration, then religion seems critical.
There are already several organizations doing exciting work in this vein, notably Effective Altruism for Christians, which has a conference every year and an impressive website; Buddhists in Effective Altruism; SARX Christians for animals; Animals in Islam; and Jewish Veg.
One obvious reason many people might not think this is an important long-term strategy is the view that as people become richer and more educated they become less religious. I think this is probably true, but at the same time, religious people have more babies, and religion continues to spread in Muslim-majority countries and maintain its hold in India. This predicts a growth in the percentage of religious people in the coming decades. The future, in short, is far from clear.
So what should we do? Is there an 80,000 Hours career profile in this? The easy idea one might have based on this argument is to do outreach to religious communities. I suspect that outreach from outsiders will be limited in its impact. A better route might be for do-gooders to convince themselves to believe (as I think is actually possible) and then to enter the clergy. Happily, this seems not to be my comparative advantage since I was raised a Jew, and Christianity and Islam seem to show the most growth potential. (Although Judaism, despite its proscription of proselytizing, seems to have some way of persisting remarkably for even more time and in the face of repeated threats.) But if you were born a Christian or Muslim and are losing your faith, stop, turn around, and become an altruistic, anti-speciesist,long-termist religious devotee.