The Americans with Disabilities Act ("ADA") has two main provisions:
(1) Employment discrimination. The ADA prohibits employers with at least 15 employees, and that are engaged in interstate commerce, from discriminating in any employment decision against a qualified individual with a disability who is able, with or without reasonable accommodation from the employer, to perform the essential functions of the job. This section of the ADA is not relevant to your question, since the woman with the dog is not an employee of the church.
(2) Public accommodations. Another section of the ADA prohibits discrimination against disabled persons by privately-owned places of public accommodation. The ADA defines the term public accommodation to include 12 types of facilities, including auditoriums or other places of public gathering, private schools (including nursery, elementary, secondary, undergraduate, and postgraduate), and day care centers.
Disabled persons are permitted to sue an organization that owns or operates a place of public accommodation that engages in one or more of these discriminatory practices. However, the ADA specifies that its public accommodation provisions "shall not apply to … religious organizations or entities controlled by religious organizations, including places of worship." As a result, most types of religious organizations are excluded from the prohibition of discrimination in places of public accommodation. The House Report to the ADA specifies that "places of worship and schools controlled by religious organizations are among those organizations and entities which fall within this exemption." The House Report further specifies that "activities conducted by a religious organization or an entity controlled by a religious organization on its own property, which are open to nonmembers of that organization or entity are included in this exemption."
It is important to note that while religious organizations are not subject to the ADA's public accommodation provisions, they may be subject to similar provisions under state or local law.