I will speak on this topic based on my own experience of having lived here in Japan for 8 years as well as being familiar with the experiences of many other non-Japanese people:
One of the most important things to note here is that Japanese society strongly encourages people not to give voice to judgements they have about people who are not in their in-group (like family, co-workers, etc). A very important aspect of the Japanese is that while they can be very judgmental, they maintain an admirably live-and-let-live outward attitude towards people they do not know well. It is rare in public to see people reprimand or criticize someone for anything.
So, to use your example of a Muslim in full hijab, I cannot imagine a Japanese person going up to and verbally accosting this person under almost any circumstances. What is very likely is that they would stare at this person, take a picture, ask them if they were too warm inside, ask them for their autograph, or other behaviors that would make this Muslim feel rather alienated, but if they were to say anything regarding that person's clothing choices it would be "wow", "that's amazing", or "look Dad, it's a strangely-dressed foreigner!" - but saying something along the lines of "I don't like Muslims" would be exceedingly rare.
That said, people from China and Korea (particularly North Koreans) are the most likely to be treated poorly, due to a sort of deep-seated racism that exists between the East Asian societies that has persisted for centuries - and current political tensions in the region are having a further effect here. Case in point.
I cannot comment on all nationalities, but black people I know have generally had good experiences in Japan because, like white people, they are considered exotic by the locals. Though, they are frequently asked questions that would be inappropriate in the United States, like "Black English is cool! Can you teach me how to talk like a black person?". It is also not uncommon for Japanese people who've been out in the sun for a long time in the summer and gotten tan to jokingly say "I look like a black person". In these ways, the Japanese have little comprehension of racial sensitivity and appropriateness that less homogenous societies have developed.
One of the biggest percentage of foreigners living in Japan are from South America (particularly Brazil), and they are the descendants of the many Japanese people who emigrated there about 100 years ago. They mostly work in factories (particularly in the Tokai region of Japan, near Nagoya). From my perspective they are not rejected by their local Japanese communities, but not wholly embraced either. They are frequently unfairly blamed by the police for crimes in the areas they live though.
On the topic of the police - it is OK in Japan for the police to stop foreigners and ask for their "papers" to see if their visas are valid. From what I understand, this is more likely to happen to other Asians, Hispanics, and Middle Easterners. My wife and I are both from the United States, however she is of Filipino decent and has been stopped on occasion and asked to show her papers. I am pasty white and have never been stopped. A guy from Iran I know has been stopped a total of 8 times in his few years in Japan, often by people from the same Police Box near his apartment.
I have never heard anything to indicate that a bald white person would experience more discrimination than a non-bald one. Lots of white lifers in Japan are missing their hair anyway!
A final thing to note is that all foreigners, regardless of ethnicity, will face institutional discrimination for bureaucratic procedures. First and foremost is renting an apartment: landlords are allowed to ask if the potential tenant is a foreigner and if so they will usually reject them -- there is no legal framework to prevent this. Rental and real estate based discrimination is probably the most rampant form in the entire country. However, if you are just traveling this will probably be no problem. Other similar forms are signing any kind of contract, for foreigners they will often ask for a Japanese guarantor because these institutions are of the opinion that anyone from outside Japan is unreliable in making payments.
Another form of guaranteed discrimination is foreign kids (regardless of ethnicity) attending public schools, however this is not really limited to Japan as kids love making fun of each other for superficial things the world over.