Shortly before the act was passed, disability rights activists with physical disabilities coalesced in front of the Capitol Building, shed their crutches, wheelchairs, powerchairs and other assistive devices, and immediately proceeded to crawl and pull their bodies up all 100 of the Capitol's front steps, without warning.[38] As the activists did so, many of them chanted "ADA now", and "Vote, Now". Some activists who remained at the bottom of the steps held signs and yelled words of encouragement at the "Capitol Crawlers". Jennifer Keelan, a second grader with cerebral palsy, was videotaped as she pulled herself up the steps, using mostly her hands and arms, saying "I'll take all night if I have to." This direct action is reported to have "inconvenienced" several senators and to have pushed them to approve the act. While there are those who do not attribute much overall importance to this action, the "Capitol Crawl" of 1990 is seen by some present-day disability activists in the United States as a central act for encouraging the ADA into law.[39]
Aloha Tatiana! I wish your questions had straightforward easy answers – and if you are government funded it kind of is. (See here: https://www.ada.gov/websites2_prnt.pdf) if you are not government funded, this is something that is currently being debated in the legal system. That being said, the WCAG 2.0 guidelines are a good set of guidelines to help protect yourself if you feel you should. (You can see more on WCAG here: https://www.yokoco.com/find-out-how-to-make-your-website-compliant/)
I should mention one caveat to all of this. Businesses that are required to comply but don't have the ability to bring their websites into compliance can provide an accessible alternative to provide the same information, goods, and services that they provide online, like a staffed phone line. The trick, however, is that this option has to provide at least equal access, including in terms of hours of operation. And, as we know, the internet is around 24/7, so good luck with that. 
Title III requires that owners of public places of accommodation give people with disabilities equal access to resources. Given that we live in 2019 and a great deal of business transactions occur online, the bar for online compliance should be higher, and companies who don’t meet basic standards are in violation, just as clearly if a company’s bathroom was too small to accomodate wheelchairs.
Additionally, in February 2018, Congress passed the ADA Education and Reform Act, a bill designed to make it harder for disabled Americans to sue businesses for discrimination. Republican lawmakers who wrote and passed the bill argue that the law will help curb “frivolous” lawsuits, while opponents have argued that this law will gut the ADA, essentially giving businesses little reason to follow the ADA guidelines at all.
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.
“The idea of equal access, equal opportunity has sort of evolved in its application from brick and mortar to eCommerce. At first, many companies were worried about the desktop experience. Now, the concern extends to both smart phones and devices.  Wherever a consumer accesses your content – whether it be directly through the web or an app – you need to be concerned about accessibility.”
The Americans with Disabilities Act (ADA) and, if the government entities receive federal funding, the Rehabilitation Act of 1973 generally require that state and local governments provide qualified individuals with disabilities equal access to their programs, services, or activities unless doing so would fundamentally alter the nature of their programs, services, or activities or would impose an undue burden.2 One way to help meet these requirements is to ensure that government websites have accessible features for people with disabilities, using the simple steps described in this document. An agency with an inaccessible website may also meet its legal obligations by providing an alternative accessible way for citizens to use the programs or services, such as a staffed telephone information line. These alternatives, however, are unlikely to provide an equal degree of access in terms of hours of operation and the range of options and programs available.
This portion of the law is regulated and enforced by the U.S. Equal Employment Opportunity Commission. Employers with 15 or more employees must comply with this law. The regulations for Title I define disability, establish guidelines for the reasonable accommodation process, address medical examinations and inquiries, and define “direct threat” when there is significant risk of substantial harm to the health or safety of the individual employee with a disability or others.  
In 2010, the DOJ issued an Advanced Notice of Proposed Rulemaking (ANPRM) called the Nondiscrimination on the Basis of Disability; Accessibility of Web Information and Services of State and Local Government Entities and Public Accommodations.  An ANPRM is not law but a published notice in the Federal Register used by an agency to feel out its proposal and get feedback/comments before making it a rule; It’s a prudent move by federal agencies to try and get everything right before making a law.
Title I of the ADA prohibits private employers, state and local governments, employment agencies and labor unions from discriminating against qualified individuals with disabilities in job application procedures, hiring, firing, advancement, compensation, job training, and other terms, conditions, and privileges of employment.  The ADA was amended on September 25, 2008, to clarify and reiterate who is covered by the law.  The ADA Amendments Act of 2008 (ADAAA), Pub. L. 110‐325, made significant changes to the ADA’s definition of “disability” that broadens the scope of coverage under both the ADA and Section 503 of the Rehabilitation Act.
Two agencies within the U.S. Department of Labor enforce parts of the ADA. The Office of Federal Contract Compliance Programs (OFCCP) has coordinating authority under the employment-related provisions of the ADA. The Civil Rights Center (CRC) is responsible for enforcing Title II of the ADA as it applies to the labor- and workforce-related practices of state and local governments and other public entities. Visit the Laws & Regulations subtopic for specific information on these provisions.
The ADA provides explicit coverage for service animals.[22][23] Guidelines have been developed not only to protect persons with disabilities but also to indemnify businesses from damages related to granting access to service animals on their premises. Businesses are allowed to ask if the animal is a service animal and ask what tasks it is trained to perform, but they are not allowed to ask the service animal to perform the task nor ask for a special ID of the animal. They cannot ask what the person's disabilities are. A person with a disability cannot be removed from the premises unless either of two things happen: the animal is out of control and its owner cannot get it under control (e.g. a dog barking uncontrollably in a restaurant), or the animal is a direct threat to people's health and safety. Allergies and fear of animals would not be considered a threat to people's health and safety, so it would not be a valid reason to deny access to people with service animals. Businesses that prepare or serve food must allow service animals and their owners on the premises even if state or local health laws otherwise prohibit animals on the premises. In this case, businesses that prepare or serve food are not required to provide care or food for service animals, nor do they have to provide a designated area for the service animal to relieve itself. Lastly, people that require service dogs cannot be charged an extra fee for their service dog or be treated unfairly, for example, being isolated from people at a restaurant. People with disabilities cannot be treated as "less than" other customers. However, if a business normally charges for damages caused by the person to property, the customer with a disability will be charged for his/her service animal's damages to the property. 
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