The Civil Rights of Act of 1866 (42 U.S.C. § 1981) was interpreted in the late 1960s as prohibiting discrimination even in private contracts based on race. In 1991, Congress expressly included that interpretation in the statute. Because in the late 1800s, "race" was understood to include what today might refer to "ethnicity" (e.g., German, Arab, Jewish), the Court concluded that § 1981 extends to such discrimination based on ethnicity.
But there is no statute generally banning discrimination in contracting (as opposed to specific kinds of contracts, like employment, housing, or public accommodation) based on religion. Section 1981, by its terms, simply doesn't cover religious discrimination.
This was the key behind Domanic v. Christian Bros. Automotive Corp., decided Wednesday by Fifth Circuit Judge Stuart Kyle Duncan, joined by Judges Andrew Oldham and Cory Wilson; an excerpt: