How to Fix the Infamous "Error sending email" on Drupal 8/CentOS 7

I had this problem recently on this site that was really baking my noodle. It turned out to be a mixture of SELinux and reCAPTCHA misconfiguration.

First, check if SELinux allows the web server to send emails from your site:

$ su -
# getsebool httpd_can_sendmail

If the boolean is off, turn it permanently on:

# setsebool -P httpd_can_sendmail 1