`react-table` is headless. I am forced to create my own html structure and am in control of the markup from the start. `headless-ui` provides those components which doesn't give me full control over markup, does it?
'headless' means you bring your own html structure, the library provides interaction and state exposed by props or hooks. As such, I am not sure Headless UI is headless since they only let you bring your own CSS. At that point, it's a lot easier to create your own set of components that you have full control over than to include another NPM dependency.
Technically Facebook/Twitter are not websites, but "social" applications (web/native). You need to have a user account to see (FB) or post (FB/Twitter) anything.