Answer: All praises due to Allah. The muslim jurists differ with regards to considering Kafa'ah (equality) of nasab (descent) in marriage. Those who say it is a condition of marriage, then they say a marriage of prophet Muhammad's descendant to a non-descendant is not binding. But the correct view is that kafa'ah is not a condition in a total sense. A Muslim cannot marry a kafir (non-believer), a chaste person cannot marry an adulterous person, and this is the extent of kafa'ah required in the Quran and the Sunnah.
If we look at books of Seerah and Islamic history, you will find a lot of instances as proofs. Zainab binti Jahsh, the prophet's aunt's daughter, who was from the noble family of Quraish, married Zaid bin Harithah, who was his liberated slave. The prophet's daughters married Othman bin Affan who was not from Bani Hashim, but from Bani Abdushams. Ali (RA) gave away his daughter, Umm Kalthum daughter of Fatimah az-Zahra, in marriage to Umar bin al-Khattab who is not from Bani Hashim. Bilal bin Rabah, the liberated slave, married the sister of Abd ar-Rahman bin Auf who was from Quraish.
Criteria to Choose a Spouse
عَنْ أَبِي حَاتِمٍ الْمُزَنِيِّ قَالَ قَالَ رَسُولُ اللَّهِ صَلَّى اللَّهُ عَلَيْهِ وَسَلَّمَ إِذَا جَاءَكُمْ مَنْ تَرْضَوْنَ دِينَهُ وَخُلُقَهُ فَأَنْكِحُوهُ
On the authority of Abu Hatim al-Muzani who said: Rasulullah (SAW) said: "If someone whom you are pleased with his religion and character comes to you (seeking your daughter in marriage), then marry him (to her)."
عَنْ أَبِي هُرَيْرَةَ رَضِيَ اللَّهُ عَنْهُ عَنْ النَّبِيِّ صَلَّى اللَّهُ عَلَيْهِ وَسَلَّمَ قَالَ تُنْكَحُ الْمَرْأَةُ لِأَرْبَعٍ لِمَالِهَا وَلِحَسَبِهَا وَجَمَالِهَا وَلِدِينِهَا فَاظْفَرْ بِذَاتِ الدِّينِ تَرِبَتْ يَدَاكَ
On the authority of Abu Hurairah (RA): The prophet (SAW) said: "A woman is married for four (traits): her wealth; her status; her beauty; and her religion. So, look for the one with religion you will be successful."
Shaikh Ibn Uthaimin (rahimahullah) said in Sharh al-Mumti': "If beauty, wealth and status are with a religious woman, then that is light upon light. If otherwise, then the one that should be sought after (for marriage) is the religious woman."
[Sharh al-Mumti' ala Zad al-Mustaqni' (12/13)]
We do not deny the status of the Ahl al-Bayt, but the status goes hand in hand with their religious conviction. If they are non-believers, then they will be in the Fire forever. But if they are muslims, they are loved and respected as much as they follow the best of them, ie. prophet Muhammad (sallallahu 'alayhi wasallam). Allah Almighty said in the Quran:
وَنَادَى نُوحٌ رَبَّهُ فَقَالَ رَبِّ إِنَّ ابْنِي مِنْ أَهْلِي وَإِنَّ وَعْدَكَ الْحَقُّ وَأَنْتَ أَحْكَمُ الْحَاكِمِينَ قَالَ يَا نُوحُ إِنَّهُ لَيْسَ مِنْ أَهْلِكَ إِنَّهُ عَمَلٌ غَيْرُ صَالِحٍ فَلَا تَسْأَلْنِ مَا لَيْسَ لَكَ بِهِ عِلْمٌ إِنِّي أَعِظُكَ أَنْ تَكُونَ مِنَ الْجَاهِلِينَ
"And Nuh called upon his Lord and said, "O my Lord! Verily, my son is of my family! And certainly, Your promise is true, and You are the Most Just of the judges.'' He said: "O Nuh! Surely, he is not of your family; verily, his work is unrighteous, so ask not of Me that of which you have no knowledge! I admonish you, lest you should be one of the ignorant.''
Ponder these verses... Prophet Nuh asked Allah to rescue his son, with the argument that his son is his Ahl al-Bayt. But look at how Allah replied! He replied in no uncertain terms, saying that "He is not of your family"!
So, even the prophet's direct son was not considered from Ahl al-Bayt because he was not righteous! Similarly, prophet Muhammad's descendants are noble and deserve respect as much as they follow the religion. If they are following the Sunnah, then they are the noblest of men.
But even so, they are not prohibited from marrying outside of Ahl al-Bayt as we have showed above that there was no such prohibitions or taboos even among the companions during the prophet's time, and after his time. And they choose their spouse based on their partners' commitment in religion.