If you are applying to some traditionally conservative specialty (like maybe neurosurgery or general surg, etc.) in perhaps a traditionally conservative institution in the South or Midwest or Northeast, you might get away with less in terms of hairstyle than you could at perhaps some urban community IM program in California. However, one would hope that if you are neat, clean and have the hair tied back, it should not matter. However, I know that beards were definitely banned at my IM residency. It was said to be about getting the respirator/Tb masks to fit right, but I also think it was about the image the institution wanted. Some places also require that male residents wear a tie, and Duke used to require all the interns to wear white pants.
It's like a lot of other things in med school and residency. It's about how much of yourself you are willing to subvert to the will of the collective "bosses" and/or the hospital or med school institutions themselves. How important is the hairstyle to you, or do you just not care that much?
Overall, I think that interviewers not "liking" things like a hairstyle is probably going to decrease over time, because a lot of the older docs are more conservative and they keep retiring. Younger people tend to allow more leeway in terms of dress, etc. Not always but usually.
I have a question, though. Isn't it necessary to wash dreadlocks? I can see how a thicker type hair would not need washing as often, but it still needs to be washed, right?