The Federal Government is compelled by the Constitution etc etc... to not engage in discriminatory practices. While not every Catholic Charities offers adoption services, would need to comply with nondiscriminatory practices. And that would also be true of funding channeled for other programs regardless of the affiliations of the NGO. 

short course on USAID.... http://web.mit.edu/urbanupgrading/upgrading/resources/organizations/USAID.html

Under methods.. 

USAID establishes partnerships with the people and governments of assisted countries, U.S. businesses, non-governmental organizations (NGOs – here defined as those in the host country), private voluntary organizations (PVOs – defined as NGOs in the United States), academic institutions, other U.S. government agencies and international assistance etc .... also
Programs are created and maintained through these partnerships.
  Over 80% of USAID’s grant funds go to United States NGOs and businesses.