The secular service has to have a clearly stated objective, that objective must be measurable, and that objective must also be something that relieves the burden of the State to care for people. If all three conditions are met, that secular service can keep its tax exempt status.
Where are you getting this? Most 501(c)3 non-profits in the US wouldn't meet that standard.
Article: Can investors make money in social services?
According to the article, six states are experimenting with funding social programs using "social impact bonds", which only pay out if the programs achieve their official objectives. The project is in its early stages, so it's not clear what will happen if the market decides that a program isn't worth funding, but this looks quite promising.