I managed to go a bit further now. I deactivated the operator and edited my StatefulSet. I added the environment variable:
- name: PROXY_ADDRESS_FORWARDING
value: "true"
Now, I suppose it is just a matter of making the Keycloak CRD configurable now. Either giving the possibility to pass any environment parameters, either having a property proxyForwarding in the CRD. Or maybe it should be linked to the existing externalAccess property?