Oh my is this topic ever familiar territory.
Showing my Crabbet-bred stallion (read: perfectly trained, perfectly well mannered and ALWAYS an angel) at open shows - same remarks. Hunting him (capped) (yes, some of of the Crabbet-bred Arabians had more jump than the Tbs against whom we often competed) with a recognized hunt, where no one noticed until standing behind him while we were trailer loading to return home - same remarks. Another stallion, many years later - identical except for size to a 2-year-old GELDING of mine; the boarding barn where I was while my home barn was being upgraded with new plumbing and wiring - self-described “trainer” took my 2-year-old GELDING out of his stall without my permission or foreknowledge and, as related by other boarders to me in frantic phone calls, started removing hair and flesh with a whip screaming all the while that “stalions need to be taught lessons.” I even got yelled at by a prospective barn helper who was not yet a legal adult when I had to inform her that my liability insurance prohibited barn help who was underage BECAUSE I HAD A STALLION. She was just sure that was because ALL STALLIONS ARE KILLERS and she was bent on making sure I knew how “stupid” I was for having a stallion on the premises. I cannot tell you how very amused and quite bored I was at being taken to task by a 17 year old who had lied about her age to get the interview and had to fess up when asked for ID.
I believe we have Hollywood to thank for this mess.