Freedom of Religion Concerns
I doubt that this policy would be held to be unlawful on First Amendment freedom of religion grounds. Indeed, such requirements usually exclude church-related service.
Also, I don't see how this policy discriminates against your religion specifically. It seems on its face to apply to all religions equally.
Even if "Church-related" is read broadly to include both service that benefits a church, and also service that is organized by a church, that doesn't preclude you from coming up with some other kind of service that is neither of these things.
Why would you be prevented from coming up with service that is neither of these things when other students do not?
Unless you have also undertaken Holy Orders or something, in which case 100% of your time away from school would be devoted to your church, it is hard to see what the problem would be with this requirement for you as opposed to someone else. And, it would probably be improper for a public school to allow you to use religious activities to satisfy a graduation requirement - that would sound like an establishment clause violation.
Some of the relevant U.S. Supreme Court cases are:
Engel v. Vitale (1962) and Abington School District v. Schempp (1963)
This pair of cases shaped the modern understanding of how the
Establishment Clause of the First Amendment constrains prayer in
public schools. In Engel, the Court struck down a New York State rule
that allowed public schools to hold a short, nondenominational prayer
at the beginning of the school day. The Court decided that these
prayers amounted to an “official stamp of approval” upon one
particular kind of prayer and religious service, and said that, since
teachers are agents of the federal government, the scheme violated the
Establishment Clause.
The reasoning in Engel was also applied in Schempp, in which the Court
struck down a Pennsylvania policy that required all students to read
10 Bible verses and say the Lord’s Prayer at the beginning of each
day. While a student could get an exemption with a parent’s note, the
Warren Court decided that this still amounted to an unconstitutional
government endorsement of a particular religious tradition.
Lemon v. Kurtzman (1971)
This case adjudicated a different sort of Establishment Clause
challenge, where the controversy dealt with a statute providing
financial support for teacher salaries and textbooks in parochial
schools. The Burger Court unanimously decided that this financial aid
scheme violated the Establishment Clause and delineated the governing
precedent for Establishment Clause cases known as the Lemon test.
Under Lemon, statutes (1) must have a secular legislative purpose; (2)
must have primary effects that neither inhibit nor advance religion;
and (3) cannot foster an “excessive government entanglement with
religion.” The Court held that this scheme violated the third prong of
the Lemon test.
Allowing Church-related community service projects could implicate both the second and third prongs of the Lemon test.
In a pertinent ruling, the Colorado Supreme Court upheld a state constitutional requirement that no public funds be used to assist religious organizations, even if this prevented a facially neutral voucher program from treating religious and non-religious schools equally. The opinion in this 2015 case reviews some of the relevant law.
A critical portion of the analysis is that aid to religious institutions must be limited to institutions that do not discriminate on the basis of religion and that supporting religious institutions at the K-12 level is more of a concern than doing so at the higher educational level. A Church, however, would (and should) discriminate on the basis of religion.
In General
There has been consideration of whether community service requirements, in general, are constitutional. Generally, courts have upheld the programs. See also here.
In particular, Rhode Island is in the 1st Circuit of the federal courts, which has expressly ruled that community service requirements are constitutional.
A 1999 law review article in the Duke Law Journal considers the issue from several perspectives. So does a 1997 Loyola of Los Angeles Law Review article. A 1916 case called Butler v. Perry is a particularly strong precedent in favor of the proposition that mandatory service is constitutional, despite arguments to the contrary under the 13th Amendment. The issue was discussed in the New York Times in a 2003 article.
Both are concerned about the involuntary servitude aspect of the requirement, but given that school attendance may be mandatory, and a community service requirement is one, relatively unconstrained aspect of mandatory educational activity, this isn't a very easy case to make.
