Actually I would not assume a white person was looking at me funny because of my skin color. I'm not even sure I would interpret the look as "funny." I read stories by black people complaining about a white people giving them "funny" looks on the subway, at the movies, at the airport, etc. About 20 years ago I used to make assumptions about--or interpret how--people were "looking funny" at me and fumed about it to my wife. She (who is just the sweetest thing on two feet) told me she didn't notice anything. I stopped all that nonsense then and now greet people on the street with a smile and a good morning, good afternoon, goood evening. Guess what? That ended a problem I had created.
Sometimes it's not easy to ignore the racist who has power; an interviewer for a job, a work supervisor, a police officer, a physician, etc. Sometimes the racism has to be dealt with. People who discriminate virtually never admit to it. However, they can be forced to ceased a discriminatory practice usually by some official channels (arrest, civil damages from a lawsuit, etc.). Often, that leads to resentment because "I'm not a racist. That isn't how my parents raised me. I have black friends." yada, yada, yada...
That written, there's no doubt in my mind that white racist attitudes towards blacks has reduced signigficantly over the past three generations.