You wouldn't necessarily have to end up with two separate domains —you probably would have the API living on a subdomain of your site (api.yoursite.com).
This is pretty standard practice for decoupled applications.
Themes are just fine, but IMO your code is more portable if you are fully broken out of WordPress (just in case you change your API from WP to something else later).
By moving to a fully decoupled approach you are losing the benefits of integrating with future third-party WordPress plugins that work with a React-based front end as well as not being able to avoid additional network requests on app initial load.
I suppose it depends on the goals of the project. Some folks would rather only use WordPress at the data source and not require any functionality from plugins (unless those plugins manipulate the data, but in that case you still wouldn't care that it's fully decoupled, because those plugins could still interact with the data within WP and never care about the frontend).
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You wouldn't necessarily have to end up with two separate domains —you probably would have the API living on a subdomain of your site (api.yoursite.com).
This is pretty standard practice for decoupled applications.
Themes are just fine, but IMO your code is more portable if you are fully broken out of WordPress (just in case you change your API from WP to something else later).
By moving to a fully decoupled approach you are losing the benefits of integrating with future third-party WordPress plugins that work with a React-based front end as well as not being able to avoid additional network requests on app initial load.
I suppose it depends on the goals of the project. Some folks would rather only use WordPress at the data source and not require any functionality from plugins (unless those plugins manipulate the data, but in that case you still wouldn't care that it's fully decoupled, because those plugins could still interact with the data within WP and never care about the frontend).