The scholars of Islam and Sunnah are in agreement (ijmā’) that it is permissible for a man or woman to marry outside of their race or tribe so long as they adhere to the Religion of Islam. The scholars also agree that it is permissible for a Muslim man to marry a chaste (morally upright) woman from the people of the Scripture (Jew or Christian) whether she is an Arab or non-Arab. However, it is not permitted for a Muslim woman to marry a Jewish or Christian man― such a marriage is invalid. 
The permissibility of marrying into a different race, nation, tribe or social background is proven through the Book, the Sunnah and the actions of the Sahābah and Salaf. Allah (the Most High) said:
يَا أَيُّهَا النَّاسُ إِنَّا خَلَقْنَاكُم مِّن ذَكَرٍ وَأُنثَىٰ وَجَعَلْنَاكُمْ شُعُوبًا وَقَبَائِلَ لِتَعَارَفُوا ۚ إِنَّ أَكْرَمَكُمْ عِندَ اللَّهِ أَتْقَاكُمْ ۚ إِنَّ اللَّهَ عَلِيمٌ خَبِيرٌ – 49:13
“O mankind, indeed We have created you from male and female and made you peoples and tribes that you may know one another. Indeed, the noblest of you in the sight of Allah is the most righteous of you. Indeed, Allah is Knowing and Acquainted.” (Al-Hujurāt: 13)
Allah has made clear in this verse that no one has distinction over another, nor virtue over another in the sight of Allah except due to taqwā, or piety. The noblest of people with Allah are the most righteous, dutiful and God-fearing. The Prophet (ﷺ) was asked regarding the noblest of people, so he replied: “They are the most righteous of them.” (Bukhāri no. 3353, Muslim no. 2378)
So the verses of Qur’an and the Prophetic Hadīth prove that between the nations and tribes and races there is equality― and it is permitted for a Qurashi and Hāshimi to marry someone from the tribe of Tamīm or Qahtān or other than them, and vice-versa.
The Prophet (ﷺ) was the best of the tribe of Quraish and Banu Hāshim, and he married Zaynab bint Jahsh (may Allah be pleased with her) and she was from the tribe of Bani Asad bin Khuzaymah, she was not a Quraishi woman. He married Umm Habībah bint Abī Sufyān (may Allah be pleased with her) and Hafsah bint ‘Umar (may Allah be pleased with her), also Juwayriyah bint Al-Hārith (may Allah be pleased with her), Sawdah bint Zam’ah (may Allah be pleased with her), Umm Salamah (may Allah be pleased with her) and ‘Ā’ishah (may Allah be pleased with her)― and they were not from the tribe of Banu Hāshim. He also married Safiyyah bint Huyayy (may Allah be pleased with her) and she was from the Children of Israel (from a Jewish tribe of Madinah).
‘Umar bin Al-Khattāb (may Allah be pleased with him) was from the tribe of Banu ‘Adiyy and he married Umm Kalthūm bint ‘Ali bin Abī Tālib (may Allah be pleased with her) and she was from the tribe of Banu Hāshim.
‘Uthmān bin ‘Affān (may Allah be pleased with him) was from the tribe of Banu Umayyah and he married Ruqayyah, and after her death, he married Umm Kulthūm (may Allah be pleased with them), both of whom were daughters of the Prophet (ﷺ) and from the tribe of Banu Hāshim.
Examples of this nature are very numerous indeed― and they all prove that the Prophet (ﷺ) and his Companions did not care about the affair of lineage, so long as the Religion of the people was firm, steadfast and righteous.
This is further proven by the fact that the Prophet (ﷺ) married Usāmah bin Zayd (may Allah be pleased with him) who was a freed slave of the tribe of Bani Kalb to Fātimah bint Qais (may Allah be pleased with her) who was a Quraishi woman. Also, Abu Hudhayfah bin ‘Utbah bin Rabī’ah bin Abdush-Shams (may Allah be pleased with him) married off the daughter of his brother to Sālim yet she was a Quraishi woman and Sālim was a freed slave.
Likewise, Abu Bakr As-Siddīq (may Allah be pleased with him), who was a Taymī-Qurashi, married his sister off to Al-Ash’ath bin Qais (may Allah be pleased with him) who a Kindī Yemeni from the tribe of Qahtān.
Also, Abdur-Rahmān bin ‘Awf Az-Zuhrī (may Allah be pleased with him) married off his sister to Bilāl bin Rabāh the Mu’adhin (may Allah be pleased with him)― she was a Zuhrīyah, Quraishi Arab woman and Bilāl was a freed slave from Abyssinia (Ethiopia).
All of this guides the students of knowledge to recognise the permissibility of marriage of a person to someone from other than his tribe, race, skin colour or social background as long as they are religious people, steadfast upon the Religion, and of course compatible for each other. The Prophet (ﷺ) said:
إِذَا أَتَاكُمْ مَنْ تَرْضَوْنَ خُلُقَهُ وَدِينَهُ فَزَوِّجُوهُ إِلاَّ تَفْعَلُوا تَكُنْ فِتْنَةٌ فِي الأَرْضِ وَفَسَادٌ عَرِيضٌ
“If there comes to you a man whose character and religious commitment you are pleased with, then marry your ward (daughter) to him, for if you do not, there will be fitnah in the land and widespread corruption.” (Ibn Mājah, 1967)
And the Messenger (ﷺ) also stated:
تُنْكَحُ الْمَرْأَةُ لأَرْبَعٍ لِمَالِهَا وَلِحَسَبِهَا وَلِجَمَالِهَا وَلِدِينِهَا فَاظْفَرْ بِذَاتِ الدِّينِ تَرِبَتْ يَدَاكَ
“A woman is married for four reasons: for her wealth, her status (lineage), her beauty and her religion, so marry the one who is religious, and you will be successful, may your hand be covered with dust.” (Muslim, 1466)
So a Muslim should look at many reasons for marrying a particular person, but the most precious reason is the religious adherence of a potential spouse. And what has been stated as proofs and examples is sufficient for any sincere Muslim.
(Based around a fatwā from Al-Imām Ibn Bāz (rahimahullāh), see Al-Jāmi’ fī Fiqhil-‘Allāmah Ibn Bāz (pp. 869-870), also Majmū Fatāwa of Ibn Bāz)
 Even worse is a ‘marriage’ between two people of the same gender― such a marriage is invalid.