Are there non-Muslim people who are forced to wear clothing over their head to avoid discrimination?
There are other religious traditions, aside from Islam, that require a head covering. Jewish men are expected to cover their heads in the synagogue or temple as a sign of humility before God. Jewish women are expected to cover their heads when around any male other than their husbands because their hair is their "crowning glory," which only a husband should be permitted to enjoy and because exposing the hair is supposed to be a distraction to other men. Many Jewish women choose to wear wigs over their own hair, while others wear a scarf of some sort. I have a student who is Rastafarian, and she keeps her head covered at all times, too. It is my understanding that the Rastafarian requirement is for women to keep their heads covered when they pray, but my student extends this to all situations. I would guess that there are other ancient and modern religions that have this requirement. It would be interesting to see what a scholar of religion could contribute on this point.
I am not aware of any tradition in which people must cover their heads to avoid discrimination, and sadly, there are many instances in which wearing a head covering elicits discrimination, as in the case recently decided by the United States Supreme Court, a case in which a woman wore a hijab to a job interview and was not hired because of it. Fortunately, the Supreme Court ruled that this was religious discrimination, but this does not prevent people, particularly in the West, from discriminating or simply thinking prejudiced thoughts on this basis.