There's nothing wrong with being afraid. We are wired to distrust anything not like ourselves. The problem comes when you act on those fears and make poor decisions.
It can be dangerous to assume that mass shooters are automatically mentally ill. More often than not they have normal brains and just choose to kill people.
After Columbine, the media went with a narrative that portrayed the shooters as bullied loners. In reality, if anything the shooters were the bullies. They weren't tormented outsiders longing to belong. They just wanted to kill for fun.
How is it not? You were talking about how people are generalizing and compared it to how people generalize black people. Being black doesn't disturb your thought process, it doesn't make you think people are going to kill you, it doesn't make you act out in belief you are defending yourself, it doesn't make you think you are a god, it doesn't make you think you are saving the world, it doesn't make you think they're talking about you on the news.
It's bad to generalize on basis of physical characteristics, yes. It's not bad to generalize people who have a common illness that disturbs their thought process, because, their thought processes are disturbed. One is not like the other. One affects behavior, one does not.
What people have a problem with isn't that you're afraid that someone with a mental disability might be violent - it's that you're afraid of ALL people with mental health issues, which is a generalization and stereotypization in very broad strokes.
The comparison to people of color is fairly apt, as that, too, is a very broad generalization and is problematic primarily because of that, and not of the fact that some members of that demographic are in fact violent (as are some members of basically any demographic you pick).
You can turn that all around, too, and ask "why do people have a problem if I'm afraid of white people?" - which I'm sure to you sounds somewhat ridiculous, but is statistically about as sound as fear of other generalizations (i.e. not all that much).
By the way, what's behind those statistics is usually also some form of generalization and/or discrimination, because even if you have accurate numbers, they don't make that much sense intrinsically. It's only when COMPARISON enters into it that they acquire their relative value, i.e. saying something like "0.2% of black people are violent" doesn't mean much until you put it in the (usually implied) comparison of "0.1% of white people are violent, therefore blacks are twice as violent as whites" (all numbers totally made up for the sake of comparison). So what you are really saying is "people X are more/less violent than people Y", with one of the two usually being the group the speaker belongs to. Thus what is portrayed as just making 'a neutral assessment based on statistics' is actually just an attempt to differentiate your own group from some other group, and, usually, to elevate your own group's perceived self-worth relative to another group.
In essence, if you're saying "I'm afraid of group A, and that's okay because they're often violent" what you really MEAN is "group A isn't worth as much as my own group/my own group is better/worth more than group A". And THAT is what people have a problem with; understandably so, I dare say, since the worth of human individuals cannot and must not be reduced to such oversimplified comparisons.
So in your opinion every mentally ill person is a homicidal, mass murdering, killing machine? I bet you think every black person ever is a thief, every hispanic is an illegal immigrant, and every person with a gun is going to shoot someone maliciously too, yeah?