"Forbidden" response when saving entry with HTML code in matrix field
There are a couple possible explanations for this.


You have Suhosin installed, a PHP extension that enhances security by placing some pretty drastic restrictions on what data can be sent to the server. To find out, visit /admin/utils/phpinfo and search the page for "suhosin". If you see any references to it, you have it installed. Ask your host to uninstall it, or possibly just configure it to be allow this specific use case (and expect to have similar requests in the future).
Your server (Apache or nginx) may be configured to deny traffic to the request URI. Check your server logs for recent forbidden/403 activity.