To separate church and private education in the manner in which you have proposed is to violate the first amendment of the Constitution.
From Loma Linda's Affirmative Action statement, which is freely available on the University's website:
"The free exercise of religion guaranteed by the constitution of the United States includes the right to establish and maintain religious educational institutions. Loma Linda University is incorporated as a California religious nonprofit corporation, owned and operated by the Seventh-day Adventist Church as an integral part of the Church's teaching ministry. Federal and state guidelines clearly recognize the right of religious institutions to seek personnel and students who support the goals of the institution, including the right to give preference to members of the church which sponsors the institution.
The University is committed to equal education and employment opportunities for women and men of all races and does not discriminate on the basis of handicap, sex, race, color or national origin in its education and admissions policies, financial affairs, employment programs, student life and services or any University-administered program. It does, however, retain the right to give preference in student admissions to qualified Seventh-day Adventist applicants. While this right is retained, it should be emphasized that admissions are not limited exclusively to Seventh-day Adventist applicants.
To this end, the University is in compliance with Titles VI and VII of the Civil Rights Act of 1964 as amended, and substantial compliance with Title IX of the Education Amendments of 1972 (45 CFR 106 et seq.) Sections 503 and 504 of the Rehabilitation Discrimination in Employment Act of 1967 and Section 402 of the Vietnam Era Veterans Adjustment Act of 1974 and does not discriminate against any employee or applicant for employment on the basis of age or because they are disabled veterans or veterans of the Vietnam era. In addition, the University administers student programs without discrimination on the basis of age, except in those programs where age is a bona fide academic qualification for admission in accordance with the provisions of the Age Discrimination Act of 1975.
The University reserves constitutional and statutory rights as a religious institution and employer to give preference to Seventh-day Adventists in admissions and employment, including but not limited to 42 USC Secs 2000e-1, 2000e-2, Sec 6-15 of Federal Executive Order 11246: 41 CFR Secs 60-1.5(5); 20 USC Sec 1681(a) (3), 34 CFR Secs 106.12(a) (b), 106.21, 106.31, 106.39, 106.40, 106.51, 106.57; California Government Code Secs 12926(d) (1); and Title II, Division 4, Chapter 2, Section 7286.5 of the California Code of Regulations, the First Amendment to the United States Constitution and Article I, Sec 4 of the California Constitution. The University believes that Title IX regulations are subject to constitutional guarantees against unreasonable entanglement with or infringements on the religious teachings and practices of the Seventh-day Adventist Church. The University expects students and employees to uphold biblical principles of morality and deportment as interpreted by the Seventh-day Adventist Church. The University claims exemptions from the provisions of the Title IX set forth in 34 CFR Secs , 86.21, 86.31, 86.40, 86.57(b)."