This is likely not due to Pi-hole blocking anything, but you can use these tools to determine if Pi-hole is blocking any of the domains that are needed to make those email servers work for you:
Just in case anyone else gets similar issues, these 3 digit codes, like "403 (Forbidden)", are sent by the web server you're trying to connect to. This means that your PC/device/phone/whatever successfully connected to the web server, and it responded with that code. In this case, 403 means "Forbidden", which can happen when a user isn't logged in or doesn't have the privileges to access that page, for example.
The fact that the remote server responded, means that the Pi-hole successfully looked up the IP address for that remote server, as it should, and did not block it, which is why it was "likely not due to Pi-hole".
If it had blocked it, you would typically see a failure to connect at all (e.g. "Can't be reached") error, as Pi-hole most commonly blocks ads by pointing your device at 0.0.0.0 for said advert, which is a non-routeable address.