@pointythings
If these animals never panic, is it alright for me to throw things at them or scream through a megaphone near them? No, even if they didn't spook, I'd be arrested because I might have spooked them, therefore I was endangering both animal and rider.
Although there is evidence to prove that they do indeed sometimes spook.
A horse spooked on Harry and Meghan's wedding day in the procession and threw his rider. That was without a megaphone. A police horse panicked during a protest/riot a few years ago and threw their rider off, seriously injuring her.
And the police had reason to believe the protestors were going to climb over the barrier. The protestors have denied this but they would do, wouldn't they?