Changing default img html markup but not in admin back-end?

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is_admin() is a call that does not verify if the current user role, but rather it was made to check if the code is trying to display in the backend/admin/dashboard area.

https://codex.wordpress.org/Function_Reference/is_admin

You can try one of three solutions:

  1. Reverse the check

        if(is_admin())  // if display on the dashboard, abort
        return;

    ..... your code

  2. Check for the user capabilities with the current user check and if the dashboard/admin is being displayed:

      if(!current_user_can('manage_options') && is_admin())
    {
     Your code
    }

  3. Check the actual roles and by default, therefore not display the admin:

    function is_this_admin_user()
  {
   return in_array('administrator',  wp_get_current_user()->roles);
  }
if(is_this_admin_user() == 0)
  {
  ....your code
  }