Conceptually, components have state, but it's all managed by react, so you only ever write pure functions. Granted, depending on how you update state in event handlers and lifecycle methods, you will need to think about state a lot, but this is an unavoidable fact of UI programming.

> every component must be created by extending a base class

This is an implementation detail, instead of ES6 classes you can also use React.createClass(), which might as well be named React.createComponent(). These "classes" can't be inherited from.

React supports stateless components, it's literally just a plain JavaScript function.

From the React docs:

> In an ideal world, most of your components would be stateless functions... This is the recommended pattern, when possible.

React is an interesting mix of functional and OO. It's OO, in that the primary approach for defining components is class-based, and components have state and lifecycles. It's functional, in that the render methods are expected to be pure functions based on component state and props, and simply output a description of what the UI should look like as a result. Also, as a whole, React definitely pushes you to view the system in terms of composition, state transformations, and pure functions, rather than imperative "toggle this, add that, update the other thing".

Not sure why people have that impression. It doesn't fundamentally do any OO things. You don't inherit from the react components. Maybe you could make an argument for encapsulation but even that is shaky in JavaScript. Most it only uses prototypes as object for namespacing and to organize the api better since JS lacks good namespacing syntax.

It depends on how you use React. You can use it in a stateful, OO way. Or you can use it in a more functional way. A good example of how to use React in a functional manner is the Redux framework (basically you don't use the stateful parts of React and treat your components as a tree of pure render functions). http://redux.js.org/