Most airlines in the United States have tightened their mask-wearing requirements, with some allowing no exemptions from the rule, other than for very young children.  Most no longer allow medical exemptions.

Hawaiian Airlines is one of the few to allow medical exemptions.  This from the Hawaiian Airlines web site:

• Guests are required to wear a face mask or covering that effectively covers the mouth and nose while boarding, through the duration of the flight and while deplaning at their destination.
• Young children unable to keep a face covering on, or guests with a medical condition or disability preventing its use, will be exempt from the policy.

Delta Airlines does allow a medical exemption, and also has strict policies on what kinds of masks may be worn.  From the Delta Airlines web site:

Plastic face shields may be used in addition to a mask but are not approved mask replacements. Any mask with an exhaust valve is not approved as an acceptable face mask for customers traveling on any Delta operated flight. 

Customers with unique mask requirements should bring the appropriate face covering that best meets their needs. Customers with underlying conditions that explicitly prevent the wearing of a face covering or mask are strongly encouraged to reconsider travel or should be prepared to complete a ‘Clearance-to-Fly’ process prior to departure at the airport. If you require this exemption, please arrive early to complete the process during check-in and avoid missing your flight – this process can take over one hour. Please arrive early to allow additional time. Mask exemptions only apply for travel on flights operated by Delta Air Lines and Delta Connection.

Any false claims of a disability or health condition to obtain an exemption from wearing a mask or face covering may result in the suspension of travel privileges on any Delta flight for the duration of the mask/face covering requirement.

Anybody flying should check the requirements directly from the airline.  Several airlines have created a “no fly” list of passengers no longer allowed to fly on that airline because of their refusal to wear a  mask.