Disable REST API Breaks Contact Form 7

Hey,
When the option “Disable REST API” is enabled for non-authenticated users Contact Form 7 is not working. Console output example:

GET https://www.myurl.com/wp-json/contact-form-7/v1/contact-forms/4948/feedback/schema 401
www.myurl.com/:1  Uncaught (in promise) Response?{type: 'basic', url: 'https://www.myurl.com/wp-json/contact-form-7/v1/contact-forms/4948/feedback/schema', redirected: false, status: 401, ok: false,?…}
Promise.then (async)
Uncaught (in promise) Error: A listener indicated an asynchronous response by returning true, but the message channel closed before a response was received

I used a different plugin to disable the REST API and didn’t have this issue before. There should be a way to exclude certain API calls from the disable option or some standard ones should not be included in the first place.

All the best,
Helmut