All or nothing is not a good way to get people together on an issue. It's perfectly possible to not be a vegetarian and not want a horse to be beaten and abused. Surely vegetarians and vegans would want everyone to object to that?
It's such a weird argument. For one thing, crops are often fertilised by manure from farmed animals, often with those animals turned out directly on to the land. Wildlife is frequently shot and killed to keep it away from crops. And then when those crops are harvested invertebrates and smaller vertebrates that cannot escape are also killed. There isn't one part of food production that doesn't involve using something from animals or killing them.
Now as far as I can work out, most vegans live with the knowledge of this on the grounds that they are at least trying to minimise their impact. Well, likewise. I try to minimise my impact. As an imperfect person who sometimes slips up, or who yes, eats cheese, I can still see that what this woman did is wrong. Start with the common ground and try to build on it, FFS.