Some Google-Books perusal suggests that airlines in the U.S., if they sell tickets to the public (rather than operating as private carriers) have an even strong

Some Google-Books perusal suggests that airlines in the U.S., if they sell tickets to the public (rather than operating as private carriers) have an even stronger obligation than public accommodations, as common carriers who are required to provide service to the general public at the stated rates without discrimination, like phone companies, railroad companies, telegraph companies, ferry boats, etc. Whereas public accommodations like hotels are only prohibited from certain enumerated kinds of discrimination (race, religion, etc.). Seems to be a concept in 18th-century English law that crossed over to the early US, and stayed around in limited contexts (transportation and communications). Admittedly, not specifically related to freedom of speech in that case.