People in religious networks give and do more than people with religious beliefs but no networks.
People who profess no religion, but who nonetheless go to church sometimes, give and do more than their co-(non)-religionists who do not go to church.
Arthur Brooks, who I have written about before, says that conservatives give and do more than liberals. Putnam and Campbell find that this is because conservatives are more likely to be religious. Secular conservatives are not notably giving or civic-minded. In fact, American Grace argues,
“According to the best available evidence, the ‘civic good guys’ are more often religious liberals, not religious conservatives.”