While legal considerations might be your biggest worry, making your site more accessible is simply good customer service. More than 39 million Americans are blind and another 246 million have "low vision," Another one million are deaf in the U.S. Add to that people with mobility issues that prevent them from using their hands and that's a huge portion of the country's buying power.
Level AA is a little more significant, and makes sites accessible to people with a wider range of disabilities, including the most common barriers to use. It won't impact the look and feel of the site as much as Level AAA compliance, though it does include guidance on color contrast and error identification. Most businesses should be aiming for Level AA conformity, and it appears to reflect the level of accessibility the DOJ expects. 

The Department of Justice’s revised regulations for Titles II and III of the Americans with Disabilities Act of 1990 (ADA) were published in the Federal Register on September 15, 2010. These regulations adopted revised, enforceable accessibility standards called the 2010 ADA Standards for Accessible Design, "2010 Standards." On March 15, 2012, compliance with the 2010 Standards was required for new construction and alterations under Titles II and III. March 15, 2012, is also the compliance date for using the 2010 Standards for program accessibility and barrier removal.
The Federal Communications Commission (FCC) enforces regulations covering telecommunication services. Title IV of the ADA covers telephone and television access for people with hearing and speech disabilities. It requires telephone and Internet companies to provide a nationwide system of telecommunications relay services that allow people with hearing and speech disabilities to communicate over the telephone.
I’ve been able to fix the problem by changing the default-calendar-grid.php file to change the contents of the buttons that they noted above. I ended up replacing the chevron icons in the file with stylized “<” and “>” characters, respectively. This allows a screen reader to see that there is actually content within the button, and furthermore within the table header, and as a result fixes the errors it has with the calendar.
Until the ADA is updated to address the special case of website accessibility, or the Department of Justice releases its website accessibility regulations, complying with WCAG 2.0 Level AA is the best way to ensure that people with disabilities have equal access to your website. The overview below is a great starting point about meeting the WCAG 2.0 Level AA recommendations.
A person’s method(s) of communication are also key. For example, sign language interpreters are effective only for people who use sign language. Other methods of communication, such as those described above, are needed for people who may have lost their hearing later in life and do not use sign language. Similarly, Braille is effective only for people who read Braille. Other methods are needed for people with vision disabilities who do not read Braille, such as providing accessible electronic text documents, forms, etc., that can be accessed by the person’s screen reader program.

In court, Netflix tried to argue that websites should not be part of ADA compliance regulations, as there is no physical structure / location. They also argued that websites should not be in scope of ADA as there is no public component (the original ADA compliance law specifically called out that ADA rules apply primarily to services, locations, and products that are supposed to be open to the public).
An accessible and ADA compliant website has the potential to increase your sales by over 20%. The market segment of persons with a disability is very loyal to businesses and websites that make legitimate efforts to increase their quality of life. Your businesses social media presence can also be improved as visitors share their favorable interactions with your businesses. Offering your business a significant and fiercely loyal revenue stream.
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