The IRS requires that certain employers offering a 403(b) plan must satisfy the universal availability requirement with respect to elective deferrals. All employees of these employers must be eligible to make elective deferrals if any employee has the right to do so, with certain limited exceptions. Certain part-time employees may be excluded from eligibility to make elective deferrals.
Universal availability for elective deferrals does not apply to a church, as defined in IRC 3121(w)(3)(A), or a qualified church-controlled organization, as defined in IRC 3121(w)(3)(B).
You can find additional information on the universal availability requirement at the IRS website.