Some people have claimed that if a potential customer without a mask attempts to enter a privately owned store/business, then the Americans with Disabilities Act makes it illegal to ask the person if they have a disability which prevents them from wearing a mask. Is this true?
The ADA does not prohibit private entities from asking potential customers about disabilities. Title I, Section 102 (c) [Medical Examinations and Inquiries] puts limits on what an employer can ask potential employees. Title III, sections 301 through 310, which covers public accommodations and services operated by private entities, does not mention medical inquiries at all.
For reference, here is the text of ADA.