There are almost too many possible uses for data science in the nonprofit sector to count. You might want to look at the question from the other way around--find a cause that interests you and see how data science would apply.
Disaster relief efforts need better modeling and forecasting in everything from anticipating possible disasters to optimizing relief efforts. How can we identify the population most at risk from natural or human-created disasters, what are the most effective ways to mitigate the risks, and during a disaster, what are the most effective ways to deliver relief?
In education, what methods work best? In a country or region with low female literacy, what would be the economic impact of increasing female literacy by a certain percentage?
For poverty relief, based on a particular area's demographics and economy, what is the most affordable way to reduce poverty? How could a funding organization recognize sooner whether an ongoing project is likely to succeed or fail?
Or if you're interested as much or more in the human aspects, you could look at ways for communities or countries to build reliable data banks, getting all of the government, nonprofit, educational, and other organizations to share and use data effectively.
I hope this helps!