I use React in a very functional way, as all my data is stored outside of React as a global JSON object, and that data is injected to a top-level component. Thus React is just a clever templating engine for me: a transformation of JSON to Virtual DOM, and then application of Virtual DOM to the real DOM. Rendering always trigger from the main component and is optimized thanks to immutability. Read more here
I don't agree with Rygu, the errors are part of the state. Stores may be comparable to databases, but what does that mean? That stores should only contain something that is not "temporary" or something that may be considered as meaningless?
For me, if you want to embrace functional programming with React, anything that is displayed as DOM should rather be in the first place passed as props of your components, including errors. If you don't, then you rely on side effects to manage the DOM, and it will be harder to reason about all these side effects over time.