The Holy Quran mentions about the Racism: 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).

"The issue of equality between all human beings, opposition to any type of racial, ancestral and class discrimination, fairness between all the children of Adam in relation to human rights and that no person is better than another due to his skin color, language, lineage or race - is one of the most important societal issues in the Qur’an which has been mentioned in various verses of this Heavenly Book. The Qur’an has denounced all sorts of superiority - whether it be of race, language, or skin color." 

Likewise, Prophet Muhammad (PBUH & HP) says: Surely all of mankind – from the time of Adam until our time – are like the teeth of a comb (all equal to one another) and there is no greatness for an `Arab over a non-`Arab and no greatness for a red-skinned person over a black-skinned person, except due to one’s consciousness of Allah (taqwa).”

There are numerous verses in the Holy Quran and the teachings of the Holy Prophet (PBUH & HP) that invite human beings towards brotherhood and equality. Throughout his life, the Holy Prophet (PBUH & HP) taught people that all humans are one and the only difference that exists is in their God-wariness as mentioned in verse 13 of Surah Hujarat. We learn from the Holy Prophet (PBUH & HP) and the Ahlul Bayt (AS) that Islam has established equality for the entire human race and struck at the very root of all distinctions based on color, race, language or nationality. According to Islam, Allah has given man this right of equality as a birthright. Thus, no man should be discriminated against on the basis of the color of his skin, his place of birth, his race or the nation in which he was born. 

Apart from conveying the pure teachings of Islam, the Holy Prophet (PBUH &HP) was also able to rouse hope in the hearts of the poor and the downtrodden section of his society. In many instances within his practical life, he was successful in eliminating bigotry and racism that was surrounding him. In order for him to reach his aim of equality between all human beings, he married the daughter of his uncle to a slave named Zaid. In addition, he gave Bilal, who was both a non-`Arab and an African slave (at one point in his life), the important religious post of being the Muaddhin, the one who calls to prayer. He also convinced Ziyad ibn Labid who was one of the richest and noblest men from amongst the Ansar to marry his daughter to an African slave named Jubair. This marriage between a nobleman's daughter and a slave, was the beginning of many such marriages that broke mental and social barriers among the followers of Islam. Islam is a practical example of how human beings and societies can fight racial discrimination and create a society based on unity and brotherhood.

Martyr Malcolm X Talks about Racism in Hajj

The annual ritual of Hajj is an outstanding display of beauty and splendor among the followers of Islam and it is this very beauty of Islam that inspired (Martyr) Malcolm X to write the following letter after he made his first Hajj:

"Never have I witnessed such sincere hospitality and overwhelming spirit of true brotherhood as is practiced by people of all colors and races here in this ancient Holy Land, the home of Abraham, Muhammad and all the other prophets of the Holy Scriptures. For the past week, I have been utterly speechless and spellbound by the graciousness I see displayed all around me by people of all colors.....There were tens of thousands of pilgrims, from all over the world. They were of all colors, from blue-eyed blondes to black-skinned Africans. But we were all participating in the same ritual, displaying a spirit of unity and brotherhood that my experiences in America had led me to believe never could exist between the white and the non-white. You may be shocked by these words coming from me. But on this pilgrimage, what I have seen, and experienced, has forced me to rearrange much of my thought-patterns previously held, and to toss aside some of my previous conclusions. This was not too difficult for me. Despite my firm convictions, I have been always a man who tries to face facts, and to accept the reality of life as new experience and new knowledge unfolds it. I have always kept an open mind, which is necessary to the flexibility that must go hand in hand with every form of intelligent search for truth.
During the past eleven days here in the Muslim world, I have eaten from the same plate, drunk from the same glass and slept in the same bed (or on the same rug)-while praying to the same Allah with fellow Muslims, whose eyes were the bluest of the blue, whose hair was the blondest of blond, and whose skin was the whitest of white. And in the words and in the actions and in the deeds of the ‘white' Muslims, I felt the same sincerity that I felt among the black African Muslims of Nigeria, Sudan and Ghana.
We are truly all the same-brothers.
All praise is due to Allah, the Lord of the worlds."

Conclusion:

The Holy Quran tells us:

"Certainly, We have honored the Children of Adam, and carried them over land and sea, and provided them with all the good things, and preferred them with a complete preference over many of those We have created." (17:70)

The Holy Quran teaches us that Islam lays down some rights for man as a human being. Every man whether he belongs to one country or the other, whether he is a believer or a non-believer, whether he lives in forest or desert, whatever be the case, he has some basic human rights simply because he is a human being, which should be recognized by every human being.

Today, the world is struggling to come to terms with equality in true sense. Racial discrimination continues to be a challenge, even for the most developed nations. However, Islam has shown the way to fight racial discrimination and create a society based on amity, love and unity. InshaAllah, the world will very soon realize that the only solution to racism lies in following Islam.

References:

1. Islamic Moral System: Commentary of Surah Al-Hujurat Ayt. Jafar Subhani
2. Malcolm X's letter http://islam.uga.edu/malcomx.html

Coexistence means living together, cooperating socially and economically of either the people of two countries to fulfill their livelihood or two individuals who might not share the same interests. In other words, coexistence includes being together, not interfering in others’ private affairs, and respecting the rights of others. Islam, which considers both the individual and social needs of human beings, offers a complete package for a thriving social life. Through its teachings, the Prophet’s (PBUH & HP) and infallible Imams’(AS) tradition (Sunnah), and the Quranic teachings, Islam has provided some clear guidelines for Muslims and the followers of other religions peaceful coexistence in the Quran. Here, we focus mostly on what the Quran offers in this regard. 

1. Justice and Beneficence in Dealing with Others for A Peaceful Coexistence in the Quran

The first point raised about the peaceful coexistence in the Quran is that Muslims should deal with non-Muslims with justice and beneficence, as far as non-Muslims have not expressed any hostility against them and don’t respond to their kindness with hatred (60:8). In Surah Mumtahina, it is said that: “Allah forbids you only in regard to those who made war against you on account of religion and expelled you from your homes and supported [others] in your expulsion, that you make friends with them, and whoever makes friends with them—it is they who are the wrongdoers.”(60:9). 

Accordingly, non-Muslims are in two groups — the first group who are in peace with Muslims and live peacefully with them. The Islamic government and Muslims of society should respect this group and recognize their rights. The second group is those who act against Muslims, Islam, and the Islamic government. Undoubtedly, they should be counteracted, and there would be no place for peace in this case [1]. That’s why Imam Ali (AS) had devoted a share of public treasury (Bayt al-mal) to help the needy people of other religions. It means that an Islamic government does not overlook non-Muslims, but recognizes their rights and supports them. (10:57) 

2. Recognizing Freedom of Thought is an Underlying Factor in Muslims Peaceful Coexistence in the Quran

Humans naturally tend to reject any imposed idea or belief. And, the Quran never orders something which opposes to human’s nature. Hence, non-Muslims are not compelled to convert to Islam (2:256), and they are free to keep their religion. In Surah An’am, Prophet Muhammad (PBUH & HP) is told that: “Had Allah wished, they would not have ascribed partners [to Him]. We have not made you a caretaker for them, nor is it your duty to watch over them.” (6:107). Based on these verses, along with some others, Islam recognizes other Abrahamic religions, and no Muslim is permitted to force any non-Muslim to accept Islamic ideas. Still, Muslims should let non-Muslims to retain their own religious views and beliefs and to live peacefully in society.

3. Peaceful Religious Discussion with Others

If Muslims want to discuss their religious viewpoints with followers of other religions, they are told: “not to argue with the People of the Book, except in a manner which is best” (29:46). It means to exchange peacefully with logical reasoning and argument. Even in their discussions with polytheists, Muslims are prevented from insulting those whom they invoke besides Allah Almighty; otherwise, they would affront Allah Almighty out of hostility (6:108) [1]. It should be noted that the aim of these discussions should be clarifying the truth and not obliging others to convert. As stated above, no one is forced to accept what we believe. This manner ensures Muslims and non-Muslims peaceful coexistence in the Quran.  

4. Islam recognizes other religions

In surah Baqara, it is stated that Prophet Muhammad (PBUH & HP) and the faithful have faith in what has been sent down to him (PBUH & HP) from Allah Almighty, and they believe in Allah Almighty, His angels, His scriptures and His apostles, and they make no distinction between any of His apostles (2:285). It means that a real believer should recognize all previous Prophets sent by Allah Almighty and what they have brought to humans from Him [2]. Besides, in Ayat 62, the followers of other religions like the Jews, the Christians, and the Sabaeans who are faithful to Allah and the Day of Judgement and act righteously are told to have their reward from Allah Almighty (2:62). This is another proof that Islam recognizes other religions. Also, it reveals that there have been faithful people among the followers of other religions who truly believed in Allah almighty according to the teachings of their faith.

5. Islam Encourages Peace-Making

In dealing with the opponents of Islam, Islam orders Muslims to accept if they offer peace and declare a ceasefire and emphasizes that: “Allah does not allow you any course [of action] against them” (4:90). In other verses, Muslims are told that: “If they incline toward peace, then you [too] incline toward it” (8:61). 

6. Marriage and Friendship with non-Muslims

Another example that demonstrates Islamic teachings promote peaceful coexistence in the Quran with non-Muslims is that in the Quran, Muslims are told that: “the food of those who were given the Book is lawful to you, and your food is lawful to them” (5:5). Besides, according to the Quran, Muslim men can marry the chaste ones from among faithful women, and chaste women of those who were given the Book before Muslims, once their dowries are paid to them (5:5). These two instances show that Muslims are free to fraternize with non-Muslims and exchange with them in society.

What has been mentioned above are only some of the many Islamic guidelines that encourage treating others kindly and behaving friendly with the followers of other religions. That makes them incline slightly towards Islam, such that after a Christian boy who had converted to Islam changed his bad behavior with his mother, the mother was attracted and converted to Islam, too. This, together with many instances of the way that Prophet Muhammad (PBUH & HP) and Infallible Imams (AS) treated non-Muslims, proves Islam's deep care for the way Muslims deal with others which should ultimately lead them toward tolerance and maintaining a peaceful coexistence as stated in the Quran.  

References:

1.  M. A. Amini, “The principle of peaceful coexistence with non-Muslims in Islam,” Ma’rifat Journal, no. 165, p. 35-52.
2.  M. H. Tabataba’ei, “Translation of Tafsir Al-Mizan, “vol. 2, p. 681.