Section 504 replies to all entities including private sectarian as well as non-sectarian schools that receive, directly or indirectly, federal funds. It does not, however, apply to entities that indirectly receive merely the benefits of federal funding, but not the funding itself.

Private schools may receive Federal funding through may different avenues, including funding for school lunch programs, anti-drug programs, programs designed for at-risk students, educational reform programs, programs designed to enable student to meet national education goals, technology grants, government contracts, government loans, etc. Further, Section 504 applies even if the private school receives the federal funding indirectly. For example, if the federal government provides a grant to a non-profit entity organized to promote education, student health, or a similar purpose, which entity reallocates some of the funding to a private school, the private school is “a recipient of federal funds” under § 504. Dupre v. The Roman Catholic School of the Diocese of Houma-Thibodeaux, 31 IDELR 129 (U.S.D.C. EDLa 9/2/99).

Upon receipt of federal funding, the recipient must comply with Section 504 with respect to all of its services and programs, even though the federal funding received is limited to a single program.

From Here.