It's not too different from other client-side frameworks
I've been doing quite a lot of development on React, on both web and native. I'm going to give this answer for the web, because React native has different accessibility concerns.
React brings a semantic, object-oriented approach to building UI's. Traditional web development involves building user interfaces from components like
React allows you to build components that resemble actual logical or semantic parts of the application and UI, like
<FlightPath>. It also allows developers to bind behaviors and data flows and states to these components. As a result, I've found that UI's tend to be FAR better composed, reusable, modular, and readable with React than with any other framework I've used in the past (Angular, jQuery Node, etc).
This is especially true for data-rich apps, where UX components have a lot of dependencies and relationships with each other, like social networking, complex filtering or data analysis, or stock trading. In these applications, the need to ensure data integrity is far more important than the need to get pixel perfect presentation right.
How does this affect accessibility?
Ultimately, React renders its components into standard HTML components in the DOM, so in other words, it renders into HTML tags for you. As such, accessibility concerns are similar to those in other frameworks like Angular:
Aria and other accessibility tags can also be rendered easily with React.
Future direction. In an indirect way, React may actually be better for future accessibility because the high composability of the UX facilitates the development of advanced widgets like voice recognition plugins, large-font rendering, etc. In React, styles are specified right next to the component logic, so for example it would be easy to have different "sight-challenged" or language settings for the site and have that propagate down into widgets who know how to render themselves within that accessibility context.
I'm not affiliated with Facebook, but I have to say that after looking at and using a large variety of frameworks in the past, I've found React to be exceptionally well designed for front-end development, especially for full-stack developers.
Keep in mind that the framework is still not yet mature, so caveats apply accordingly...the set of components is still limited, security implications haven't been fully thought out, and there may still be issues with client-side memory management, etc.
Also, the collocation of behavioral logic, styles, and rendering structure into a single JSX files presents some challenges for large team development since designers and developers may need to be adjusting the same file at the same time. There are good ways around this, and IMO the advantages of collocating components into one encapsulated file far outweigh the drawbacks.