Hello,
I have a Mikrotik CCR1036-8G-2S+ that I have really been getting my head around and locking down our school network.
I have tried everything possible to block iMessage, but it seems to break Apple TV's and other Apple systems when I implement the block.
I have been doing some hunting around and lots of people are having success with a Layer 7 block.
Can someone please point me in the right direction to get this done on the Mikrotik here? I have the luxury if a 2nd box to test it on.
Any help would be amazing, thank you!

Maybe there are specific Domains for iMessage servers?
You could set static DNS records with 127.0.0.1 for it?