Hello. I am a white American male with dreadlocks and after traveling to Japan twice, I have not experienced any problems. She may run into some people who are fascinated with her dreads and want to ask questions or touch them, but that's it. I did not notice any Japanese, excluding maybe children, staring rudely or treating me differently due to my hairstyle. If a Japanese does respond poorly then he/she is probably a rude person to begin with and is not worth worrying about. Such a person's behavior would not be inspired by national/cultural customs.

However, I have not tried applying for a job or apartment yet. I cannot speak for those scenarios.

Hope that helps. : P