The rule of thumb I would use for an “accessibility” permission is: if the application’s purpose is specifically for disabled people (like a screen reader or magnifier for blind people), and you are disabled, then you should choose Yes. In all other cases always click No. Accessibility tends to be a “back door” permission that allows apps to do all sorts of powerful things they shouldn’t, like read the contents of everything you type and scrape the screen. “Normal” apps should never ask for accessibility. If they are, their developer is likely up to no good.
Dropbox, for example, was recently in the news for silently granting itself accessibility permission, and Apple had to update the OS to prevent them from doing it. They still beg users to grant them this, even lying (EDIT: misleading users) on their web page about the purpose of the permission [1].
1: https://help.dropbox.com/installs-integrations/desktop/mac-p...
[EDITed instead of replying because HN limits the number of posts I can make for whatever reason.]