Accessibility is about making web pages work for uses in a variety of stress cases. These can be caused by disabilities, injuries, environments, or situations. Here are some common and useful ones to keep in mind. Bear in mind lots of these may overlap.
Many places won't have strong Internet, like rural areas or airports with patchy hotspots. Testing on deliberately slowed connections can help you prepare for this.
Heavy pages can take unacceptably long to load. Keep page loads as light as possible.
Assets may not load. Semantic HTML can help people basically find their way around the site, even if images and styling don't load.
Visiting lots of pages will take too long. Make the navigation and its language direct. People can quickly get where they need to with fewer page visits, and therefore less pages to load.
A common stress case is using a website outside on a mobile phone. This introduces any number of obstacles users will often hit.
High or low light conditions. Address this with proper color contrast and zoom-friendly styles. If you want to really test this, put your phone as a low-quality projector in a bright room. Also test without your glasses on.
Being in a public area without headphones, like a library. Video or audio content should have subtitles or transcripts, which lets them access the content without disturbing others.
Carrying something in one hand as they walk. Mobile and touch friendly layout helps users still do what they need.
People may be in a hurry. Make sure the most important site functions can be done fast, or have options for quicker completion. Or make it easy to pause and resume long interactions. As a bonus it helps with cognitive stress cases related to short attention spans.
Everyone gets sick, at one time or another, in one way or another. It can be permanent or temporary, but will affect how you use websites regardless.
Hands could be numb or harder to move, due to soreness, numbness from anesthesia, or motor-function disabilities like arthritis. Large hitzones and simpler navigation helps here. Test for it by using a site with really thick gloves, especially with a mouse.
Another big testing method here is only using a keyboard. Focusable styles and the order of navigation elements come into play more here.
Any mode of transport, public or private, will lead to lots of stress cases.
Trains, planes, and cars can get bumpy. Interactive elements should have large-enough hitzones to lower incorrect clicks or touch gestures. Make sure it's responsive on a wide range of screen sizes, at least horizontal and portrait view.
Shaky or slow Internet, due to low quality or large use volume. See "Slow Internet" above.
People often pause and resume interactions while traveling. Include ways to easily pause or save processes for long forms. Notifications with updates or reminders also helps.
Include options for disabling motion effects. If those kick in while on a moving or shaking vehicle, it can make almost anyone queasy.
People may hold their phones awkwardly, like with straight arms. It could also be to avoid people looking at their phones in cramped travel spaces, or for physical stress cases like arthritis. Making large target areas and minimizing/turning off animations and motion helps a lot.
Users going to new sites also falls under stress cases, since it has a few specific issues on its own.
Users have trouble finding what they want at first. Direct language, simple navigation, and user-tested homepages make it easy to find things fast and with little prompting. If it takes even a few seconds too long, they'll try another site.