Theoretically that might be true but it doesn't work that way in real life. Hatred messes up your ability to tell the difference between people who are members of what you hate and those who are not. If you hate people who are gay, you probably hate people who you think are gay but actually are not. If you hate Muslims, you probably hate people who you think are Muslims but actually are not. And if you hate Mexicans, there is a good probability you don't actually know what Mexicans even look like. So naturally, if you passionately hate Nazis, you probably will also end up hating people you think are Nazis but actually are not. I have seen examples of all of those things happening in real life.
Theoretically that might be true but it doesn't work that way in real life. Hatred messes up your ability to tell the difference between people who are members of what you hate and those who are not. If you hate people who are gay, you probably hate people who you think are gay but actually are not. If you hate Muslims, you probably hate people who you think are Muslims but actually are not. And if you hate Mexicans, there is a good probability you don't actually know what Mexicans even look like. So naturally, if you passionately hate Nazis, you probably will also end up hating people you think are Nazis but actually are not. I have seen examples of all of those things happening in real life.