I would have the code handling user registration on example.com
immediately send an https
request to exampletwo.com
(which authenticates it based on certificates, of course) meaning "add this user with these credentials". This approach seems to be workable for any two web servers / frameworks / languages as long as they're able to send and receive HTTPS requests and authenticate certificates.
If you can't authenticate certificates, you could send the "add this user" message encrypted (as long as the two sites can share a secret to use for the encryption). This may be vulnerable to replay attacks, but if you make a timestamp part of the "add this user" message, you can highly restrict the time window of vulnerability for the replay attacks, probably enough to make this approach viable.
If you can't safely share secrets between the two sites, not everything is lost: you can still use public key encription. The sender encrypts the "add this user message" (including the timestamp of course) with its own private key, then with the receiver's public key; the receiver decrypts what it receives with its own private key, then with the sender's public key. A bit messy and perhaps a bit slow, but under such difficult constraints it's surprising that it can still be done at all;-).