In a word, no. The Air Carrier Access Act (ACAA) is very clear on that issue.
According to the law, qualified individuals with a disability are permitted to bring their assistive devices on board the aircraft. Additionally, an assistive device does not count towards the airline’s baggage limit. So they can’t charge an “extra bag fee” for it.
And since an assistive device is defined as “any piece of equipment that assists a passenger with a disability to cope with the effects of his or her disability”, a shower chair certainly qualifies.
So what if an airline tries to charge you to carry your shower chair? First ask to speak to the Complaints Resolution Official (CRO). This person is specially trained in the ACAA and the resolution of disability-related complaints. All US airlines are required to have a CRO available during operating hours.
That should solve your problem right there, but if it doesn’t, then you’ll have to ramp it up a notch and contact the Department of Transportation. And the good news is, they have a dedicated hotline for disability issues – (800)-778-4838.
I agree that in this day and age access should be a seamless experience, but unfortunately that’s not the way it always works. Sometimes you just have to stand up for your rights.