This is oversimplified. Freedom of religion by itself does not directly correlate to poverty reduction. The link to economic growth is indirect and reliant on the idea that countries that respect individual freedoms tend to create more open and favorable environments for investment and trade. Religious freedom can foster a more stable and inclusive environment, which indirectly supports these goals, but it is not a singular or definitive cause. The Berkley Center at Georgetown studied this idea intensively, and did find positive correlations when the whole ecosystem is taken into account. Regardless, championing (truly neutral) freedom of religion is important.

Full contextual analysis of Section 2.6: Agency for International Development here.