Inbound SMS from Twilio not showing up in CiviCRM (getting 404 error on HTTP POST)
The callback path shown in your Twilio debug is

/civicrm/sms/callback?provider=org.civicrm.sms.twilio


For WordPress, this needs to be

/?page=CiviCRM&amp;q=civicrm%2Fsms%2Fcallback&amp;provider=org.civicrm.sms.twilio


The former is suitable for Drupal CMS, but won't work in WordPress CMS. WordPress paths for CiviCRM callbacks are generally /?page=CiviCRM&amp;q=civicrm/callback/here

Per wiki: Setting up a SMS Provider for CiviSMS, the callback URL to use for Twilio/WordPress seems to be:

https://www.example.org/?page=CiviCRM&amp;q=civicrm%2Fsms%2Fcallback&amp;provider=org.civicrm.sms.twilio


Try adjusting the settings for callback over on Twilio and see if that fixes it?