I attacked a Zombie Pigman with the newly added crossbow, and the Zombie Pigman did not react at all. What I expected to happen was for the Pigman to be hostile towards me, and for the rest of the surrounding Zombie Pigmen to also begin attacking me. However, what actually happened, was that no such interaction took place, and that none of the Pigmen, even the one that I shot, reacted to my attack. 

 In my experimentation, the problem takes place when the Pigman is shot with either a normal bow or a crossbow. I was using the normal default arrow as ammo. I tried attacking the Pigman once more, but this time with a snowball, and that did trigger the expected hostile reaction. Also, to clarify, the Pigmen do react aggressively to normal melee attacks, like using a sword or fists. The glitch took place in survival mode, and I have been able to successfully repeat the glitch by attacking the Pigmen using a bow or crossbow.