Two Definitions of Racism

Ok, before I get started on the content of this post, I want to say I am sorry if I offend anyone--I am against racism and sexism, but I think that only through a clear conception of racism can we eliminate it.

It seems to me, when people use the words 'racism' and/or 'sexism', they use it in different ways. And this isn't necessarily true of just the uneducated, either. In both of my interpretations of the definition of racism, I have heard and read scholars use them in each way.
This is an exercise in Folk Philosophizing (see below), so obviously I have no real scientific evidence behind why I take these to be the definitions people are using--it just seems that way to me. So feel free to comment and criticize me.

The first definition of racism is the type that states that all stereotypes of a group of people (whether it be race or sex, or even something else) are false, and therefore, believing these stereotypes to be true is damaging ethically and practically. Now this is the definition I held about racism/sexism for almost all of my life. For example, I criticize people for saying gay men are more sensitive, have better fashion sense, are shallow, are feminine, etc. According to this definition of racism/sexism, shows like Queer Eye and Will and Grace are homophobic (or homosexist, if that might be a word), because they perpetuate these stereotypes of gay men.

But this definition of racism/sexism seems problematic. For one, I have heard many people applaud shows like Queer Eye and Will and Grace for bringing more homosexuality into the media. They don't think those shows are homophobic--this is something I have heard not from ignorant people, either, I am talking about gay men themselves applauding these shows.
The second problem with this definition of racism/sexism is a little more controversial. Let's say a sociologist did a study on gay men and found that they rank significantly higher on some kind of sensitivity scale (just work with me here, this is theoretical). Wouldn't this justify the homophobia? I mean it wouldn't prove that all gay men are more sensitive, but it would give me a rational reason to, when meeting a gay man, guess that he is more sensitive. It would be parallel to this less controversial example: I like metal music. I like Meshuggah. Now if I meet someone else who likes metal music, I am going to assume there is statistically a higher chance that this person likes Meshuggah. Now if I meet a homosexual male, I can already know that there is a statistically higher chance that he is more sensitive.
And this could work for anything. A black male is more likely to go to prison than a white male, and from this I could rationally assert, when seeing a black male on the street, that he is a criminal.
So if this first definition is right, there are empirical tests that could be done that could make racist/sexist beliefs rational. And we certainly don't want to say that racism and sexism are rational.

The second definition I hear people use seems more bizarre to me: The second type of racism/sexism assumes certain stereotypes to be true about certain groups of people, but says that disciminating against these people because of these characteristics is wrong. For example, I'm not sure if anyone remembers last year when there was a big issue with the Visitor's locker room at Kinnick Stadium, but suddenly, after years of it being, some feminists and homosexual advocates accused the University of Iowa of being sexist/homophobic because the Visitor's locker room is painted pink. Now they can't possibly using 'sexist' or 'homophobic' in the way the first definition describes it, because it wouldn't make sense. The pretense in their accusations was that pink is a color associated with women and homosexuals, so using it in this negative way is sexist/homophobic.
But this definition seems even more problematic. Using this line of reasoning, someone could say something as ridiculous as this: "Playing highly rhythm based music in clubs is racist against caucasians, because caucasians aren't born with the amount of rhythm that African Americans are." Now we certainly would accuse the speaker in this statement of him/herself being the racist for taking the pretense that white people don't have rhythm to be true.
Secondly, it does not seem so crazy to dislike a group because they hold a certain characteristic like the ones being used. If a study shows that teenagers are all rude and a bunch of thiefs, can someone really accuse me of being irrational for not liking teenagers? I don't think so, it seems a clearly valid argument:
I dislike people who are rude.
Teenagers are rude,
Therefore, I dislike teenagers.
And we can run an argument like that for any 'accepted' stereotype. For example:
I dislike people who love the color pink.
Women tend to like the color pink.
Therefore, I tend to dislike women.

As we can see, both ways in which people use the words 'racism', 'sexism', and 'homophobia' seem flawed. But I can't find any way to resolve it. I am much inclined to try to fix the first definition, because it seems much closer to what most people mean by these terms than the second, but I'm keeping an open mind. Any ideas?