Note that the above mostly applies to company/product specific component libraries where maintaining design/brand consistency is of great importance. For components meant for public consumption, I personally would only use libraries that yield _all_ rendering decisions to the user: not just styling, but the components being rendered as well as the way in which those components are composed.

Usually that means providing state & handlers through a render prop API, so users can compose their own styled components in arbitrary arrangements that wouldn't be possible with an interface that only exposes specific component overrides inside of a rigid structure. See downshift as an example of a library that does this really well (https://github.com/downshift-js/downshift), and contrast that to something like react-select that only offers the ability to provide overrides for specific components in its own predefined render tree (https://github.com/JedWatson/react-select).

Perhaps on top of that you can also provide a reasonable styled default, but not offering low level control of rendering is usually a deal breaker in my book when picking third party components to work with.