Is it normal to react to racism differently depending on the situation

When people act racist against my race, I tend to react differently depending on the reasons. I usually don't feel insulted if the reason is because of direct personal effects, for example if some storekeeper was repeatedly robbed by them or if they were particularly unkind directly to them. So I don't get offended if someone says stuff like "I hate [race] because they invaded my land and killed my family" or "Because I was raped by one as a child".

But I get really insulted if they start generalizing because of something that doesn't affect them directly, such as people turning racist just because they saw several videos of people of my race doing something bad to someone else. (ex. "I hate [race] because they rape their babies" or "Because I saw some video of them killing horses").

For example, I wouldn't feel offended if a someone started hating my race because they were a victim of a genocide or political quarrel that people of my race did, but I would feel very insulted and angered if someone uninvolved bystander of another race turned racist against and started generalizing my race because he heard the reports or saw some videos of the atrocities.

Is it normal to react this way?