They've also given over $150 million to the Islamic Development Bank to support their vaccine efforts and smaller amounts to dozens of other Muslim-based groups for different initiatives. Likewise for Jewish organizations.
B&MG Foundation are incredibly results driven, all of their grants come with direction for measuring impact and reporting on it. They aren't giving to religious organizations to further religion, but because those organizations are best suited to reach the most people or best suited to responsibly steward enormous amounts of money and resources.
*He should improve contraception instead*
Given 1000 donors donating a million vs 1 donor with a billion (as somebody else points out below) you could imagine such biases being averaged out ...
For example political campaign donations are obviously zero-sum, as is lobbying for mutually exclusive well-intentioned causes.
For example suppose that we want to do a cost-benefit analysis to see if convincing people to use contraception is a more effective charitable intervention than whatever Gates is doing.
If the Catholic Church really hates contraception, they would oppose that. They might tell Catholic charities to refuse to work with Gates. They might spend a little money and a lot of cheap labor on convincing people to not use contraception. Generally they will spend resources on doing the opposite thing and Gates would have to spend more resources just to cancel out the Catholic influence.
Since we know beforehand that this is very likely to happen, we should include that in the cost part of our cost-benefit analysis. It's possible Gates did just that and concluded that working with Catholics instead of against them is better.
I tried looking for similar grants to religious services organizations from other religions, but my search came up empty. Very happy to stand corrected on this.