Racism and ethnocentrism are closely linked to the sense of superiority that lies within every human being. This issue has a long history - as long as human life, and is still an ongoing behavior that causes serious problems among human beings.

Racism is an important issue that Islam has considered; the issue whose history dates back to nations existed long before the birth of Prophet Muhammad (PBUH&HP). This unequal treatment was so weaved into people’s lives which they didn’t even realized its vile nature. Prophet Muhammad (PBUH&HP), also, lived in a society where racism was very common. The situation became even harder when people started to follow the religion of Prophet Muhammad (PBUH&HP). That was when racism out of tribal prejudice was extended to segregation based on religion, and many people who followed Prophet Muhammad (PBUH&HP) were driven from their homes or hometowns. 

The specific conditions of the era in which Prophet Muhammad (PBUH&HP) lived, as well as the deep roots of this wrong attitude in the history of humankind, were the main reasons why Allah (SWT) makes many recommendations about racism in the Quran. The Prophet of Islam (PBUH&HP), also, worked really hard to clear the minds of people from tribal, religious, and any other types of racism.

What does the Quran and Prophet Muhammad (PBUH&HP) say about Racism?

During the Arab ignorance, privileges such as lineage, race, wealth, number of children, and affiliation with a powerful tribe were considered the criteria of superiority over others. The verses of the Quran indicate that the number of children and folks were so important to them that in some arguments they even went to a cemetery and started to count the number of their dead ones:

 “Rivalry [and vainglory] distracted you until you visited [even] the graves.” (102: 1-2) 

It should have been hard for people of that mindset to accept that their lineage, children, tribe and wealth is of no importance in the eyes of Prophet Muhammad (PBUH&HP). According to an account, he said, “All the people, from the past or at present, are as equal as a comb’s teeth; therefore neither Arabs are superior to non-Arabs, nor white people to blacks. You are only distinguished by your piety and righteousness” [1]. 

However, although the Quran was revealed in such an environment that was limited in various ways and had a limited connection with the world outside the island, and the issue of ethnicity, race, and tribal life prevailed in all its aspects, it did not take on such a color at all. Allah addresses people in the Quran using the following phrases: "O children of Adam," "O people," "O you who believe," or "O you who have faith." The Quran removed racial privileges in that racist environment, and with the beautiful logic of "you are all children of man and were created from one parent," Allah declared them all brothers and sisters belonging to the same family:

“O mankind! Indeed, We created you from a male and a female and made you nations and tribes that you may identify yourselves with one another. Indeed the noblest of you in the sight of Allah is the most God wary among you. Indeed Allah is all-knowing, all aware.” (49:13)

As the verse above implies, One’s character and status are only measured by the level of submission to Allah and following His commands, not social or financial conditions. 

Religious Discrimination 

Apart from racism based on lineage, race, wealth, etc. people before and at the time of Prophet Muhammad (PBUH&HP) believed that religious beliefs gave them superiority over others. 

Based on that belief, people of different faiths were always conflicting with each other, instead of having sound arguments about different issues. Therefore, religious discriminations had been severely condemned by Islam, emphasizing that belonging to the followers of religion does not make people good or bad. But, it is their actions and their level of obedience toward Allah that give them superiority: 

“The Jews say, ‘The Christians stand on nothing,’ and the Christians say, ‘The Jews stand on nothing,’ though they follow the [same] Book. So said those who had no knowledge, [words] similar to what they say. Allah will judge between them on the Day of Resurrection concerning that about which they used to differ.” (2: 113)

The Quran on sexism 

The issue of fairness and justice among human beings is so important in Islam that the Quran has taken care of all different aspects in which people may act unjustly toward each other. Apart from racial issues that have been ongoing for ages, the issue of undermining and suppressing women in different domestic and social aspects, and depriving them of their rights had been a challenging issue in most parts of the world. 
The Quran condemns this segregation and states that men and women are equal in the eyes of Allah: 

“Whoever acts righteously, [whether] male or female, should he be faithful, We shall revive him with a good life and pay them their reward by the best of what they used to do.” (16:97)

Also, the necessity of observing women’s rights had been emphasized in many narrations from Prophet Muhammad (PBUH&HP) and his progeny. Imam Ali (AS), says in an account, “Women are Allah’s trusts upon you, do not hurt them, and do not put pressure on them” [2]. Therefore, men should be careful with their manners in treating women whether in family or in society. 

To conclude, the only thing that gives superiority to people is their piety and faith. Looking at the issue like this makes people closer to each other and all differences in color, race, ethnicity, shape, wealth, etc. create no distance between people. People gather around based on their spiritual interests and try not to judge each other, since the only one who is aware of the most faithful is Allah (SWT): 
“… And be wary of Allah. Indeed Allah knows best what is in the hearts.” (5: 7).

References:

1. Al-Shaykh Al-Mufid, Al-Ikhtisas, p.341.
2. Muhaddith Nuri ,Mustadrak al-Wasail, vol.2, p.551.