This is particularly important when working for a government agency or government contractor, as these organizations must follow web accessibility guidelines under Section 508 of the Workforce Rehabilitation Act of 1973. Although ADA and Section 508 compliance are different, the published checklist for Section 508 compliance offers insight into ways to make websites accessible for people with disabilities, and thereby work toward ADA compliance.
This guidance document is not intended to be a final agency action, has no legally binding effect, and may be rescinded or modified in the Department's complete discretion, in accordance with applicable laws. The Department's guidance documents, including this guidance, do not establish legally enforceable responsibilities beyond what is required by the terms of the applicable statutes, regulations, or binding judicial precedent.

WordPress themes designed with accessibility in mind tend to be easier to use and clearer to navigate than their contemporaries. While you may have specific goals in mind like ADA compliance or WCAG 2.0 standards to pass, rest assured that you won’t have to sacrifice on design quality. You’ll likely find a theme with a higher standard of design by searching for templates with these requirements.

In many situations, covered entities communicate with someone other than the person who is receiving their goods or services. For example, school staff usually talk to a parent about a child’s progress; hospital staff often talk to a patient’s spouse, other relative, or friend about the patient’s condition or prognosis. The rules refer to such people as “companions” and require covered entities to provide effective communication for companions who have communication disabilities.
@Rick, I didn't specifically look at doctype, but Steve Faulkner did in his original article (see the link at the top of this post). He found that 101 of the 130 pages containing role="main" (78%) used the HTML5 doctype, which of course leaves 22% that didn't. I do recommend using ARIA even if using an earlier doctype. Validation is important, but if validation and accessibility conflict, I think most would agree accessibility should trump validation. Assistive technologies that support ARIA landmarks do so regardless of doctype, and otherwise the presence of these role attributes has no ill effects in any user agent.
Most recently, however, pizza chain Domino's has been brought under suit for their website not being accessible for specialty ordering. The U.S. Supreme Court refused to review the case, instead upholding the decision of the 9th U.S. Circuit Court of Appeals who said the “alleged inaccessibility of Domino’s website and app impedes access to the goods and services of its physical pizza franchises—which are places of public accommodation.”

The Americans with Disabilities Act (ADA) was first passed in 1990. Twenty years later, the US Department of Justice released an update called the 2010 ADA Standards for Accessible Design. These standards cover the design of physical spaces and have been interpreted to include web locations as well, so it can be difficult for the would-be accessible website designer to use them.