Hi @enchiridion, thanks for reaching out to us aboout this.
According to WordPress themselves:
The REST API is a developer-oriented feature of WordPress. It provides data access to the content of your site, and implements the same authentication restrictions — content that is public on your site is generally publicly accessible via the REST API, while private content, password-protected content, internal users, custom post types, and metadata is only available with authentication or if you specifically set it to be so. If you are not a developer, the most important thing to understand about the API is that it enables the block editor and modern plugin interfaces without compromising the security or privacy of your site.
Our security researchers are always hunting for exploits in WordPress and available plugins in order to keep the millions of Wordfence websites safe. Whilst they have found REST vulnerabilities in specific plugins for developers to patch in the past, the API itself is extremely safe.
The information that is available via the WordPress REST API is already available to the public via other means, such as the website itself and RSS. The only difference between the front-end of the website, RSS and the REST API is the way the data is presented. As long as you keep your WordPress version up to date, along with your plugins and themes, you should not have any problems.
Ultimately, Wordfence Central requires access to the REST API for users who aren’t logged in, so that’s one of the first things I’ll check on a website when a customer has issues connecting.
If you decide to allow access, head over to Wordfence Central, go to the Connection Issues tab. Clear out any sites that might be in here.
Now head back to your site and log in as an admin. Navigate to Tools > Diagnostics > Other Tests > Clear all Wordfence Central connection data. Clear the connection data and then from the Wordfence Dashboard, click on “Connect this site” in the Wordfence Central widget.
https://www.wordfence.com/help/central/connect/#troubleshooting-connection-issues also has some troubleshooting steps you could follow.
Thanks,
Peter.