It's vital that we make library websites for all people who want to use them. Libraries have an especially wide range of patrons and people who would be patrons if they had access. (When we talk about online accessibility, it's common to use the numeronym "a11y" since it's short. See internationalization, "i17n".) Accessibility has been the base of the web from day one.
A11y isn't something that we can drop in last minute on a website, it's a process phase that requires our full attention during the coding of a website. There are different levels of a11y coding outlined in WCAG specifications, and a myriad of rules that we have to ensure pass. An easy, basic rule is that every image needs alternative text so that a visitor could know what's in the picture if they can't see it. Another easy, basic rule is there needs to be enough contrast between colors so that text and headlines are readable. Every rule gets progressively more detailed and can only be understood as part of a whole system to make sites the most usable to the most people.
The dark side of a11y is that in many ways it's never done, and there's not one-stop place that will check compliance of every rule. There's plenty of tools that will check a site's alternative text, text contrast and other basic compliance, but too many of the rules are contextual and only human testing ensure the site passes. And the WCAG rules change over time, and browsers do, too, so even if a site passes validation now, it might not in a year or two. A11y is a learning process for everyone, and very large companies with large staffs of a11y folks are still learning new ways to make sites better, so even at the best case, the work will never be 100%.
And because a11y is so much work, it's common to see a11y plugins that overlay a page that are sold to "solve" a11y. They don't. While a plugin could to basic efforts like changing colors to be high-contrast, or adding a dark mode to a site, these are all done programmatically and not by a designer who would also match brand, say. More importantly, a plugin isn't going to solve big picture issues like keyboard or screen reader navigation and WAI-ARIA tags that make sense.
One of the best parts of a11y coding is that the site works better for search engines and bots that help a site be seen or indexed properly. Even the alternative text is understood as valuable to a search engine, including as "knowledge graph" information that shows up as a sidebar or above the search results on Google, or as an answer for Siri, Alexa or OK Google. Happy accident, but worth the mention.