But an assigment cannot be accessible to everyone by definition. You can't have a vision-based test accessible to a blind person as you can't have a sound-based test accessible to a deaf person.
So I'm not a disability advocate, but I did date someone who was so I was immersed in it, but never having studied it so take my answer as a best effort trying to piece together from memories.
I think the answer would be to make assignments multi-faceted that can be approached differently. Like instead of having students write a report on book they read, which priveledges the those with sight, non-dyselxics, and those that can type let them perhaps record a podcast, film a YouTube video, draw a webcomic etc that lets students show what they know. And then reflect on why does it have to be a book that's read? It could be a film, a mini-series, a radio-play, a graphic novel, a play. That allows people to approach it using their abilities instead of being hampered by disabilities such as blindness, deafness, ADHD, dyslexia, being non-verbal, etc.
It means you've distilled the assignment to it's core: can you summarise the plot, identify key moments, recognise themes and metaphors, and place the work within the historical context in which it was produced.
There you have an assignment that is much more accessible.
The tricky part is that marking them objectively is much more difficult because the criteria of evaluation are not necessarily monolithic but need to take into account the student and the mediums chosen.
It's still separate assignments. The only difference is wether you throw them into a single meta-assignment. Or a separate one with main + fallbacks.
The problem with such assignment is it's very hard to balance the alternatives to be equal. Reading a book takes quite a bit longer than watching a film or even mini-series. IMO it's perfectly fine for someone blind to watch a film and then make a report on it. But how many healthy people would just go for a film since it's quicker? And reading a book is quite a bit different experience than a film due to much more space for imagination and interpretation in a book.
P.S. calling people with no disabilities „privileged“ is just... wrong. It's not a privilege to have a set of eyes/hands/etc.