This may have been as simple as an official opening or closing prayer, expanding to Biblical lessons contained within rituals, and rules regarding behavior that are modeled on various Christian, or Jewish strictures.
Over time, traditional (~original) fraternities and sororities have relaxed some of the wording of their rituals and codes to allow a more pluralistic model and open membership to a broader group of collegians.
Similarly, Catholic nationals and locals merged, began opening chapters on non-Catholic campuses and to welcome students of Protestant heritage.
Some organizers, assuming that the traditional GLOs lacked sufficient moral guardrails in pursuit of social programming, emerged to create the first objectively Christian (Protestant, then Evangelical) fraternities and sororities.
Sigma Alpha Omega is now governed by a separate national president and board of trustees, and has grown to include 33 chapters throughout the country.
"Phi Lamb" was founded by women who saw value in the brotherhood exemplified by Beta Upsilon Chi and wished to create a female counterpart, since ΒΥΧ was a male-only organization.