Yes, as of 2018 websites absolutely must be ADA compliant.  Its a new but very scary issue that has flared up over the last year and is set to cause a LOT of turmoil.  The Supreme court issued a judgement that opened up a loophole and opportunity-chasing lawyers are aggressively soliciting handicapped people and convincing them to sue unsuspecting website owners (pretty much every website owner on the planet, as not a single one of us were ADA compliant before now.)
Technology is changing, and many website designers are using creative and innovative ways to present web-based materials. These changes may involve new and different access problems and solutions for people with disabilities. This Chapter discusses just a few of the most common ways in which websites can pose barriers to access for people with disabilities. By using the resources listed at the end of this Chapter, you can learn to identify and address other barriers.
The Department has assembled an official online version of the 2010 Standards to bring together the information in one easy-to-access location.  It provides the scoping and technical requirements for new construction and alterations resulting from the adoption of revised 2010 Standards in the final rules for Title II (28 CFR part 35) and Title III (28 CFR part 36).
ADA website compliance is about making sure that everyone has equal access to all the elements on your website and apps. That may mean you need to provide alternatives for some of the functions and content on your site in order to meet ADA website compliance standards. Here’s a quick rundown of some of the accommodations that need to be incorporated into your website to meet the ADA guidelines:

The Americans with Disabilities Act (ADA) was developed in 1990 and is meant to ensure that people with disabilities have the same opportunities as anyone else. This means any businesses that serve the public must make sure their building accommodates people with disabilities of various kinds. And now that the internet is so widely used, ADA compliance also applies to websites and even mobile apps. Basically, this means that your website needs to be accessible to people who have disabilities that affect their hearing, vision or physical capacities.

Yes, all websites must have hand rails in the rest rooms, ramps in lieu of front porch stairs and elevators with doors wide enough for wheelchairs to be easily loaded into them. Seriously though, ADA only covers Americans, and the Internet is hardly just an American institution. Besides, browsers can already be configured to override the web designer’s pre-configured fonts, font sizes, font and page and page background colors, etc, to make it much easier to read. Also, the big 3 Operating Systems (MS Windows, MAC, and Linux) have text-to-speech programs which will allow the computer to read...
I am passionate and dedicated designer tackling complex problems and finding creative solutions. I use language & content strategy to make design solutions that are intuitive, trusted, and easy to use. I put the users of my solution at the center of every decision I take. I have 5+ years of commercial projects experience at Ukrainian IT companies and 4 years at Upwork freelancer platform (projects with small budgets). Now I live in NYC area.
Most web designers offer a wide variety of services to make your website aesthetically pleasing and easy to use. Modern web design must be mobile-friendly and scalable, capable of expanding to include a blog, social media sites, and even video streaming; web designers are experts at integrating various web technologies. They can build the site, add functionality, test it, launch it on a live server, and track and maintain its performance.

If posted on an accessible website, tax forms need to be available to people with disabilities in an accessible format on the same terms that they are available to other members of the public – 24 hours a day, seven days a week, without cost, inconvenience, or delay. A staffed telephone line that sent copies of tax forms to callers through the mail would not provide equal access to people with disabilities because of the delay involved in mailing the forms.

The words in the tag should be more than a description. They should provide a text equivalent of the image. In other words, the tag should include the same meaningful information that other users obtain by looking at the image. In the example of the mayor’s picture, adding an “alt” tag with the words “Photograph of Mayor Jane Smith” provides a meaningful description.

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.
I recently finished a training in ADA compliance for websites. It was illuminating and daunting, as I realizated that there’s a lot of work to be done. It also reiterated—in no uncertain terms—a gospel I’ve been preaching for several years now. Sites need to be accessible for everyone on every platform. Previously I was just focusing on responsive sites (sites that reformat for the device used, such as a phone or tablet.) Since responsive sites are de rigueur these days, I’d like to focus on your site’s accessibility…can it be accessed by people with disabilities? This includes screen readers and other technology. It’s not just a nice thing, it’s a civil law.
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.
This particular lawsuit amounted to nothing more than a shakedown for cash, as the current laws would make it difficult to win the suit in court (more about this later) but it prompted me to dive deeper into the issue of ADA compliance. Through my research, I discovered there are some new laws on the horizon that could make ADA compliance mandatory, which means web designers and digital marketers need to know how to prepare.

Every year numerous lawsuits are taken against businesses that fail to follow the ADA’s proposed requirements for web accessibility. This failure occurs because organizations, including state and local government entities, fail to read the ADA Best Practices Tool Kit.8 They also do not follow the most up to date version of the WCAG.9 These two failures are not only detrimental to people with disabilities who want to effectively browse the web, but they are also inexcusable in today’s digitally driven world.
Web designers often design in such a way that does not allow the user to adjust font size or color. While they may be protecting their brand, they are also inhibiting some users. Many visually impaired need to use high contrast color settings or very large fonts to read a website. Don't design your website in a way that makes it impossible for them to do this. 
You are correct, ADA defines an “employer” as any person who is 1) engaged in an industry affecting commerce; 2) employes 15 or more full-time employees each work day; and 3) for at least 20 or more calendar weeks in the year. In the context of physical spaces, ADA would not apply to companies with fewer than 15 employees. However, courts don’t seem to have come to a consensus on what digital compliance really should look like. Because websites can be accessed anywhere in the country, small business owners might potentially face lawsuits in unfavorable jurisdictions. If you are a small business owner, I would recommend consulting with an accessibility lawyer and ask what they recommend.