This is a great question. It comes down to discrimination: when is it reasonable or unreasonable?
That's what the job specifications are for. They screen out people who don't have the skills you think are required for the job. Race is not typically one of them because believing people cannot do a job because they are black is based on racism views against black people.
But when you make friends you do discriminate. You may screen out people who don't have your sense of humor, or shared interests or even don't live near to you etc etc.
Now onto dating. I would say that who you date is the area of the greatest discrimination that you will do. You look at attraction, long term potential, values, everything. There are people you would work with that you wouldn't date. There are people you would be friends with that you wouldn't date.
So I think it's not unreasonable to honestly feel that you are not attracted generally to a particular race.
BUT I actually think this woman made a pretty racist statement. Here's why: I can generally not be attracted to something but I still judge people that I meet on their own terms. I don't treat them as part of a mass racial blob. This woman met a black guy, didn't find him attractive. She doesn't have to like the guy. She could have easily stated "because I don't find him attractive" - which is 100% true.
But instead she said "I normally don't prefer black guys". I think that's dehumanizing and honestly weird. "Normally" means that she likes some black guys? If so, then so why bring up the fact he's black he's at all? Why not just say she thinks he's not attractive? She's not talking about all guys in general, she's not talking about a distant celebrity, she talking about a person she's met and talked to. It's really really weird to me.
And honestly, there is a difference between head and mouth and some things are actually ok to think but rude to say. Like, a guy may not be attracted to fat women. I think that's a lot of guys. I think that's their choice but men who harp on about how they want women to be skinny honestly come across as annoying and sexist.