By Shaykh ’Abdul-’Azeez Ibn ’Abdullaah Ibn Baaz
Compatibilty is only based upon Religion and Piety:
From the evil and reprehensible matters is that some who claim to be from the tribe of Haashim [i.e. claim to be a Sayyid; someone related to the Prophet’s (sallallaahu alayhi wa sallam) family] say that there is no marriage compatibility (kafaa‘ah) between them and someone from outside of their own clan. So they do not get married outside of their clan, nor allow anyone from outside of their clan to marry them. This is a great error, a monstrous ignorance, oppression against the woman, and it is a legislation which neither Allaah nor His Messenger (sallallaahu alayhi wa sallam) legislated or prescribed. Rather, Allaah - the Most High - said:
“O mankind! We have created you from a male and female, and have made you into nations and tribes; that you may know one another, Indeed the most noblest of you with Allaah is the one who has the most taqwaa (piety, fear, and obedience of Allaah).” [Sooratul-Hujuraat (49): verse 13]
“Indeed the Believers are but brothers.” [Sooratul-Hujuraat (49): verse 10]
“The Believers - men and women - are allies and protectors, one to another.” [Sooratut-Tawbah 9:71]
“So their Lord accepted from them their supplication, and responded: Never will I allow to be lost the actions of any of you, be they male or female. You are one to another.” [Soorah Aali-’Imraan 3:195]
Allaah’s Messenger (sallallaahu ’alayhi wa sallam) said:
"Indeed there is no excellence for an arab over a non-arab, nor for a non-arab over on arab, nor for a white person over a black one, nor for a black person over a white one, except through taqwaa (piety and obedience to Allaah). The people are from Aadam, and Aadam was from earth." 
The Prophet (sallallaahu ’alayhi wa sallam) also said:
"Indeed my awliyaa‘ (friends and allies) are not the tribe of so and so. Rather my friends and allies are the muttaqoon (those who possess taqwaa) - wherever they may be." 
The Prophet (sallallaahu ’alayhi wa sallam) said:
"If there comes to you a person whose Religion and character are pleasing to you, then marry him (i.e. give the girl in marriage to him). If you do not do this, there will be fitnah (trial and discord) and great fasaad (corruption) upon the earth."
This was related by at-Tirmidhee and others, with a hasan isnaad (good chain of narration). 
The Prophet (sallallaahu ’alayhi wa sallam) married Zaynab bint Jahsh of the Quraysh (i.e. the Prophet’s clan) to Zayd Ibn Haarithah, his freed slave. He married Faatimah bint Qays from the Quraysh clan, to Usaamah, the son of Zayd. Bilaal ibn Rabaah, the Ethiopian married the sister of ’Abdur-Rahmaan Ibn ’Awf of the Quraysh. So the purpose here is to explain the falsehood of those who claim that it is forbidden, or detested, for someone from the Prophet's (sallallaahu ’alayhi wa sallam) clan to marry outside of that clan or tribe. Rather, what it is obligatory in this matter is to consider only Religion as the compatibility factor. So the Prophet (sallallaahu ’alayhi wa sallam) distanced Aboo Taalib and Aboo Lahab (his uncles) - because they were not Muslims and drew near Salmaan the Persian, Suhayb the Roman, and Bilaal the Ethiopian. This is because they possessed eemaan (faith) and piety, and they followed the Prescribed Laws and traversed the Straight Path. Thus, whosoever adopts this false and ignorant practice of barring Haashimee women from marrying from outside of their clan or tribe, will only achieve blameworthy results; such as corruption of the people, or adversely affecting the birth-rates, even though Allaah - the Most High - said:
“And marry those amongst you who are single, and the righteous from your slaves. If they be poor, Allaah will enrich them out of His Bounty. And Allaah is all-Sufficient for His creation, the all-Knowing about their state.” [Sooratun-Noor (24): verse 32]
So He commanded to marry those that are single, and to marry all other categories of Muslims - irrespective of whether they be rich or poor. Thus, since the Islamic Sharee’ah urges and encourages the institution of marriage. So the Muslims should hasten to fulfill this command of Allaah and of His Messenger (sallallaahu ’alayhi wa sallam) when he said:
"O youths! Whosoever amongst you has the ability to marry, then let him do so; for it lowers the gaze and restrains the private parts. But whosoever does not have the ability then let him take to fasting; for indeed it is a shield for him."
Its authenticity has been agreed upon.  Thus, it is incumbent upon the guardians to fear Allaah concerning their guardianship, since it is an amaanah (trust and responsibility) around their necks, and Allaah will question them concerning this trust. So it is upon them to hasten in getting their daughters, sons, and sisters married, to the extent that this task has taken full effect in life, and the corruption and harms of not doing so have been minimized. And it is known that when women are prevented from getting married, or if their marriage is delayed and deferred, then this is a cause for calamities to occur, a cause for shameful moral crimes to take place, and a cause for a decline in standards of behaviour. So - O worshippers of Allaah - it is upon you to fear Allaah regarding your own selves, and with regards to the daughters, sisters, and other women whom Allaah has been placed under your charge and authority, and that the Muslims should come in order to realise the good and the happiness for the society, and to follow the path that will increase the good and lessen the crimes. And you should know that you will all be questioned and held to account about your actions, as Allaah - the Most High - said:
“By your Lord! We shall call them all to account for all that they used to do.” [Sooratul-Hijr (15): verse 92]
And Allaah - the Mighty and Majestic - said:
“And to Allaah belongs all that is in the heavens and the earth, that He may punish those who do evil with that which they have done; and reward those who do good with Paradise which is best.” [Sooratun-Najm (53): verse 31]
So hasten in getting your sons and daughters married, following in the footsteps of your Prophet (sallallaahu ’alayhi wa sallam), and the footsteps of the noble Sahaabah (Companions) (radiyallaahu ’anhum), and all those who follow their path and guidance. I also advise you all not to seek excessive sums for the mahr (dowry), but rather be moderate in this, and that you strive to select pious and righteous people for marriage.
We ask Allaah to grant us the understanding of the Religion; grant us firmness upon it; and that He protects us and all the Muslims from the evil promptings of our own souls, and our evil resultant actions; and that He keeps away from us the deviating trials and discords, whether open or hidden. And we ask Allaah also to correct all those who have a position of authority over the affairs of the Muslims, and that He rectifies them. Indeed he is the One having the power to do so. And may Allaah extol and send blessings of peace upon Muhammad, and upon his Family, Companions and all those who follow them.
 Majmoo’ul-Fataawaa wa Maqaalaat Mutanawwi‘ah (3/100- 103)  Saheeh: Related by Ahmad (5/411). It was authenticated by Ibn Taymiyyah in Kitaabul-Iqtidaa‘ (p. 69)
 Related by al-Bukhaaree (10/351) and Muslim (no.215), from ’Amr Ibnul-’Aas (radiyallaahu ’anhu)
 Hasan: Related by at-Tirmidhee (no. 1085), from Aboo Haatim al-Muzanee and Aboo Hurayrah (radiyallaahu ’anhumaa). It was authenticated by al-Albaanee in Irwaa‘ul-Ghaleel (no. 1868).
 Related by al-Bukhaaree (4/106) and Muslim (no. 1400), from Ibn Mas‘ood (radiyallaahu ’anhu)