In many React applications, components are separated into independent "controller"-layers and "view"-layers (containers and components are nomenclature I see occasionally, but the important takeaway is that both inherit from the React component class). Business logic has no place in your view components, of course, but is quite appropriate in your controller components. I don't think component implies view layer here. Even redux actions, when used, are appropriately called from the controller layer and not the view layer. Redux doesn't change anything about logical separation of concerns.
When the Flux pattern was originally introduced, it was driven home that it should not be used for everything. redux-thunk seems to encourage that you use it for everything. What do you use when global state is not necessary (or wanted)?