A made-up example can be unfair to a kind of person without naming anyone real.

You can wrong a category without naming a person. The invented example that features a certain kind of person behaving badly does real work in shaping how listeners see actual people who resemble it, and the fact that nobody was named provides no protection. Fictional examples have non-fictional effects.

So watch the examples you reach for when making a point. Who is cast as the fool, the obstacle, the cautionary case. Try inverting the roles and see whether the argument still works. If it only lands with a particular kind of person in the unflattering position, the example is doing something other than illustrating.