Open Ports and Network Config Needed For Home Sharing
As mentioned in this Apple support document the following ports have to be open:

Home Sharing uses TCP port 3689 and UDP port 5353 to communicate with shared iTunes libraries.

Additionally port 123 (TCP/UDP) has to be open to set the time automatically. 

This is a list of all ports for Apple-related protocols, in case there are any remaining issues - Apple KB: TCP and UDP ports used by Apple software products