The American with Disabilities Act (ADA) does NOT require the acceptance of, or accomodation for, emotional support animals (ESA). The ADA, however, does not apply to air travel.

The Air Carrier Access Air (ACAA) DOES require the acceptance of ESAs with a few restrictions. You can read the applicable sections of the act in 14 CFR 382.117/.

US Airlines are generally somewhat less restrictive than the ACAA requires but they have been tightening up their requirements recently as the number of ESAs have grown. A concerned flyer can contact their airline(s) and encourage them to enforce the allowable restrictions under the ACAA.

The ACAA is a DoT regulation. Those who believe the ACAA to be too lenient can contact the DoT with their comments as well as their national representatives. Both the DoT and Congress have the power to amend the ACAA with additional restrictions.