Mr Avast team Full Member, your answer is disapointing : no solution after 5 months -> did you really try hard enough ?
I have lost a couple hours trying to find the fix, and I suspect many people have done so, because it is exasperating not to be able to use Airplay for a silly firewall issue...
So after a lot of trial & errors in the application part of the firewall settings (iTunes, "Bonjour service" and other Apple related services), the straightforward solution is in the policy part of the firewall settings:
You just need to create a new policy that allows protocol UDP on port 5353.
If this is not clear enough, I will post a screen copy when I understand how to do this...
Gerard - have a good day with music on Airplay !