I'm glad a vegan posted this (I'm not a vegan)! My problem with the article posted in the OP is that it sounds as though some activist groups that don't know much about birds of prey complained to the organisers, who also don't know much about birds of prey, on uninformed principle, and the organisers gave in and cancelled the event because they don't want the aggro. So an event got cancelled not because of actual considered evidence that the birds of prey are harmed, but because someone was ideologically loud.
I went on a short falconry course after attending a few displays, and was fascinated to learn about the history, the modern uses of falconry (crop protection in agriculture, and keeping birds away from airport runways, were two I didn't know about), and the ecological aspects (e.g. public-health-oriented laws that govern the immediate removal of roadkill have had an inadvertent severe impact on the native vulture population in this area). Like the PP, I learned that the birds are very choosy about which handlers they are willing to work with, and under which circumstances, and if they don't want to fly for some reason, or don't want to return to the handler, then they just won't.
The falconry centre to which I went does a lot of work with conservation, rehabilitation of injured birds, looking after birds that can't be rehabilitated, and education. Of the birds used in flying displays, only a few are used for courses where you learn to handle them, and those few are chosen on the basis of their willingness to engage with strangers. There is no force involved.