Have a look at Cause Hub - http://launch.causehub.io/ It has just come out of the UK based social good incubator Bethnal Green Ventures and is working with charities such as Amnesty International and Friends of the Earth.

i mean, there are a lot of public interest advocacy groups that accept donations online, but i don't think they fall under the category of start up, and i think most of their funding comes in larger donations from individuals and orgs they have relationships with.