BjornW

RESTless is a tiny WordPress plugin which disables access to the REST API (available in WordPress since version 4.4) for non-authenticated users. 
This prevents usage of the REST API by the general public and limits access to those with login credentials. No REST for the wicked.
It also supports WordPress Multisite installations.
<h3>Notes</h3>
Credits:
Sword icon used in the WordPress plugin repository and found as /assets/icon* 
From the series <a href="http://www.toicon.com/series/sketchy" rel="nofollow ugc">‘Sketchy’</a> By <a href="http://www.toicon.com/authors/1" rel="nofollow ugc">Shannon E Thomas</a>
Thanks Shannon E Thomas and to[icon] for sharing your work!
WordPress repository banner image found in /assets/banner*:
Orginal painting: <a href="http://hdl.handle.net/10934/RM0001.COLLECT.319230" rel="nofollow ugc">‘Draak’</a> 
Drawn by: <a href="https://en.wikipedia.org/wiki/Utagawa_Kuniyoshi" rel="nofollow ugc">Utagawa Kuniyoshi</a> 
Dated around 1808 – 1861 
Repository: Rijksmuseum.nl 
Modified by: <a href="https://burobjorn.nl" rel="nofollow ugc">Björn Wijers</a>
Thanks Rijksmuseum!

RESTless

RESTless disables REST calls for non-authenticated requests.

Jeff Starr

This plugin does one thing: disables the WP REST API for visitors who are not logged into WordPress. No configuration required.
This plugin works with only 22 short lines of code (less than 2KB). So it is super lightweight, fast, and effective.
Note: This plugin completely disables the WordPress REST API. So it is not recommended if you need the WP REST API for any functionality.
<h3>Features</h3>
<ul>
<li>Disable REST/JSON for visitors (not logged in)</li>
<li>Disables REST header in HTTP response for all users</li>
<li>Disables REST links in HTML head for all users</li>
<li>100% plug-and-play, set-it-and-forget solution</li>
</ul>
The fast, simple way to prevent abuse of your site’s REST/JSON API
How does it work? That depends on which version of WordPress you are using..
WordPress v4.7 and beyond
For WordPress 4.7 and better, this plugin completely disables the WP REST API unless the user is logged into WordPress.
<ul>
<li>For logged-in users, WP REST API works normally</li>
<li>For logged-out users, WP REST API is disabled</li>
</ul>
What happens if logged-out visitor makes a JSON/REST request? They will get only a simple message:
“rest_login_required: REST API restricted to authenticated users.”
This message may customized via the filter hook, <code>disable_wp_rest_api_error</code>. Check out <a href="https://wordpress.org/support/topic/not-entirely-for-non-techies/#post-12014965" rel="ugc">this post</a> for an example of how to do it.
Older versions of WordPress
For WordPress versions less than 4.7, this plugin simply disables all REST API functionality for all users.
More information available below in the FAQs section.
<h3>Privacy</h3>
This plugin does not collect or store any user data. It does not set any cookies, and it does not connect to any third-party locations. Thus, this plugin does not affect user privacy in any way. If anything it improves user privacy, as it protects potentially sensitive information from being displayed/accessed via REST API.
Disable WP REST API is developed and maintained by <a href="https://x.com/perishable" rel="nofollow ugc">Jeff Starr</a>, 15-year <a href="https://plugin-planet.com/" rel="nofollow ugc">WordPress developer</a> and <a href="https://books.perishablepress.com/" rel="nofollow ugc">book author</a>.
<h3>Support development of this plugin</h3>
I develop and maintain this free plugin with love for the WordPress community. To show support, you can <a href="https://monzillamedia.com/donate.html" rel="nofollow ugc">make a donation</a> or purchase one of my books:
<ul>
<li><a href="https://wp-tao.com/" rel="nofollow ugc">The Tao of WordPress</a></li>
<li><a href="https://digwp.com/" rel="nofollow ugc">Digging into WordPress</a></li>
<li><a href="https://htaccessbook.com/" rel="nofollow ugc">.htaccess made easy</a></li>
<li><a href="https://wp-tao.com/wordpress-themes-book/" rel="nofollow ugc">WordPress Themes In Depth</a></li>
<li><a href="https://books.perishablepress.com/downloads/wizards-collection-sql-recipes-wordpress/" rel="nofollow ugc">Wizard’s SQL Recipes for WordPress</a></li>
</ul>
And/or purchase one of my premium WordPress plugins:
<ul>
<li><a href="https://plugin-planet.com/bbq-pro/" rel="nofollow ugc">BBQ Pro</a> – Blazing fast WordPress firewall</li>
<li><a href="https://plugin-planet.com/blackhole-pro/" rel="nofollow ugc">Blackhole Pro</a> – Automatically block bad bots</li>
<li><a href="https://plugin-planet.com/banhammer-pro/" rel="nofollow ugc">Banhammer Pro</a> – Monitor traffic and ban the bad guys</li>
<li><a href="https://plugin-planet.com/ga-google-analytics-pro/" rel="nofollow ugc">GA Google Analytics Pro</a> – Connect WordPress to Google Analytics</li>
<li><a href="https://plugin-planet.com/head-meta-pro/" rel="nofollow ugc">Head Meta Pro</a> – Ultimate Meta Tags for WordPress</li>
<li><a href="https://plugin-planet.com/simple-ajax-chat-pro/" rel="nofollow ugc">Simple Ajax Chat Pro</a> – Unlimited chat rooms</li>
<li><a href="https://plugin-planet.com/usp-pro/" rel="nofollow ugc">USP Pro</a> – Unlimited front-end forms</li>
</ul>
Links, tweets and likes also appreciated. Thank you! 🙂

Disable WP REST API

while the plugin si deadsimple and very low resource impact, keep in mind that there are plugins that need the rest to work with no auth (ex. contact form 7).

dead simple and efficient, but be aware

Disables the WP REST API for visitors not logged into WordPress.

RESTless vs Disable WP REST API