It depends how you define "civic institution" but if political parties count, then China's Communist party wins the prize
Defining "civic institution" is a little tricky especially if an organisation has multiple roles. I'd argue that political parties are civic institutions even if they also have a dual role when they are in government (this is consistent with the definition given in wikianswers thanks to @ChrisW for the link). The benefit of including political parties is that it allows us to include some of the biggest recent contributions to poverty reduction in the world.
The other definitional issue is the definition of poverty. Here, however, there are widely agreed definitions such as this one from the Economist summarising a widely accepted World Bank definition:
The threshold for dire poverty in developing countries is set much lower, at $1.25 a day of consumption (rather than income). This figure is arrived at by averaging the poverty lines in the 15 poorest countries, not because $1.26 spells comfort. This is the yardstick by which poverty reduction in poor countries is measured.
On this yardstick, the world has made amazing progress on reducing poverty in the last few decades. The chart, from another Economist article, summarises recent progress and projections:
The article also summarises just how much progress has been made (I've highlighted the parts relevant to this question):
The country that cut poverty the most was China, which in 1980 had the largest number of poor people anywhere. China saw a huge increase in income inequality—but even more growth. Between 1981 and 2010 it lifted a stunning 680m people out poverty—more than the entire current population of Latin America. This cut its poverty rate from 84% in 1980 to about 10% now. China alone accounts for around three quarters of the world’s total decline in extreme poverty over the past 30 years.
What is less often realised is that the recent story of poverty reduction has not been all about China. Between 1980 and 2000 growth in developing countries outside the Middle Kingdom was 0.6% a year. From 2000 to 2010 the rate rose to 3.8%—similar to the pattern if you include China. Mr Ravallion calculates that the acceleration in growth outside China since 2000 has cut the number of people in extreme poverty by 280m.
By any reasonable statistical standards the world has made astonishing progress in the last 40 years.
Why is this relevant here? Even without doing a detailed analysis of the contributions of the Catholic Church to education and health, it is a mathematical impossibility that they could have lifted a larger number of people out of poverty. We could argue that these numbers are the result of government action, not civil institutions. And they are, but the government actions in China were the result in a change in the ideology of the Chinese Communist party, so arguably the consequence of a change in a civil institution first (though the party-government distinction is blurred in China).
But there are other stories of poverty reduction where the church might have a problem keeping up. Another Economist article reminds us that Bangladesh used to be a basket case:
Its people are crammed onto a flood plain swept by cyclones and without big mineral and other natural resources. It suffered famines in 1943 and 1974 and military coups in 1975, 1982 and 2007. When it split from Pakistan in 1971 many observers doubted that it could survive as an independent state.
Yet over the past 20 years, Bangladesh has made some of the biggest gains in the basic condition of people’s lives ever seen anywhere. Between 1990 and 2010 life expectancy rose by 10 years, from 59 to 69. Bangladeshis now have a life expectancy four years longer than Indians, despite the Indians being, on average, twice as rich. Even more remarkably, the improvement in life expectancy has been as great among the poor as the rich.
Further it is worth noting some of the key factors behind this progress is built on:
- Family planning was made free and widely accessible
- Primary education was made nearly universal (and radically improved for women)
- There was a dramatic improvement in agricultural productivity
- Microfinance gave access to loans to the poor
- The role of NGOs, especially BRAC (originally the Bangladesh Rehabilitation Assistance Committee) became significant
The focus on Women's education and freely available contraception led to one of the most profound demographic shifts in world history (with a total fertility rate--that is average number of children per woman--moving from 6.3 in 1975 to 2.3 in 2010, just above the replacement rate). The benefit of this shift in reducing poverty and mortality is not expected to be replicated in church-run programmes.
But the role of BRAC, a civic institution on most definitions, is worth noting:
BRAC began life distributing emergency aid in a corner of eastern Bangladesh after the war of independence. It is now the largest NGO in the world by the number of employees and the number of people it has helped (three-quarters of all Bangladeshis have benefited in one way or another). Unlike Grameen, which is mainly a microfinance and savings operation, BRAC does practically everything. In the 1980s it sent out volunteers to every household in the country showing mothers how to mix salt, sugar and water in the right proportions to rehydrate a child suffering from diarrhoea. This probably did more to lower child mortality in the country than anything else. BRAC and the government jointly ran a huge programme to inoculate every Bangladeshi against tuberculosis. BRAC’s primary schools are a safety net for children who drop out of state schools. BRAC even has the world’s largest legal-aid programme: there are more BRAC legal centres than police stations in Bangladesh.
The world has seen enormous numbers of people taken out of poverty in the last few decades. But the biggest numbers are attributable to Chinese economic growth arguably the result of the changed ideology of a political party. Other third world countries have also seen major improvements. But some of the key causes of those improvements are not the sort of things any catholic program could endorse (e.g. the case of contraception in Bangladesh). Other NGOs (Bangladesh's BRAC, for example) have lifted very large numbers from poverty. Compared to these numbers it is a major stretch to argue that the Catholic Church could be anywhere near the top of the league table however much good it has actually done.