If they share an ideological backbone, certainly questions will be raised about where the social services organization ends and the terrorist organization begins and what the level of connection is that is bridged by their shared dogma. Government funding of services managed by faith-based organizations is not entirely out of step with the Constitution. It is how those services are implemented that threatens to cross the line between religion and politics. In an ideal world, where everyone agrees and lives in harmony, the separation of Church and State might not be necessary. This world we live in, however, is populated by individuals who have distinct beliefs with which they were raised or which they came to through experience.
Few individuals share purely identical belief systems.
This makes it rather dangerous to entrust social work to organizations that might try to impose their particular belief system upon others. Not only is this a violation of our individual rights, but it is a situation that might prevent the aid entrusted to a particular organization from being delivered per such organization's agreement with the government.