If Jesus was of the tribe of Judah, with both his parents of the lineage of David, and John the Baptist's parents of Levi's tribe, Luke 1.5, how is it possible that John and Jesus could be related, Luke 1.36?
According to the Bible, Elizabeth (mother of John the Baptist) and Mary (mother of Jesus) were related. Luke 1:5 says that Zechariah belonged to the priestly division of Abijah and his wife Elizabeth was also a descendant of Aaron. Luke 1:36 says that Elizabeth was a relative of Mary. Here is an extract from an article that explains how this is possible - https://www.gotquestions.org/Mary-lineage.html
An argument sometimes put forward by those who deny the credentials of Christ is that, if Mary was Elizabeth’s “cousin,” then Mary must also have been a Levite. Some translations, such as the KJV, do state that Mary was the “cousin” of Elizabeth (Luke 1:36). However, the English word cousin does not have to imply a close relation, and other versions of the Bible translate the word as “relative” (NKJV, NIV, ESV, CSB, BSB).
Even if Elizabeth and Mary were close relatives, it was still possible for them to be of different tribes, as women were identified with their father’s tribe, not their mother’s. Elizabeth’s father was a Levite, making her a Levite by birth, but her mother may have been of Judah. Conversely, Mary’s mother may have been a Levite and kin to Elizabeth’s family, while Mary’s father was of Judah. Luke’s genealogy shows that Heli, whom we assume to be Mary’s father, was a direct descendant of Judah, not Levi. In addition, the angel Gabriel affirmed Jesus’ Judean lineage, telling Mary that “he will be very great and will be called the Son of the Most High. The Lord God will give him the throne of his ancestor David” (Luke 1:32, NLT). David was of the tribe of Judah.
The Bible does not say if Elizabeth was Mary’s cousin, aunt or other relation. We do know, however, that Elizabeth was getting on in years when she became pregnant while Mary was a young woman. Regardless of how Mary and Elizabeth were related, Jesus is a descendant of David and Judah:
Hebrews 7:14: For it is evident that our Lord was descended from Judah....
Revelation 5:5: And one of the elders said to me, “Weep no more; behold, the Lion of the tribe of Judah, the Root of David, has conquered, so that he can open the scroll and its seven seals.”
From this article:
The Bible doesn’t explicitly describe Elizabeth as Mary’s “cousin.” Instead, the term “relative” or “kinswoman” (sungenis, συγγενίς) is used. Many scholars seem to agree that the use of this term indicates that Mary and Elizabeth were cousins.
Could they be cousins yet be from different tribes? Here is an article about matrilenear descent in Israel:
If the reckoning of a person's tribal affiliation is matrilinear, then intermarriage between a man of one tribe and a woman of another must choose the tribe of the mother. Thus if Elizabeth's father was of Judah and mother of Levi, then Jesus and John could be first cousins. If the intermarriage were further back, then second or more distant cousins. We have no records concerning this, so it is conjecture.
Elizabeth (mother of John the Baptist) and Mary (mother of Jesus) were not related. Being not related by blood, however, is not to say the two did not know each other.
Luke 1:5 tells us that Zacharias (father of John the Baptist) married Elizabeth who was a daughter of Aaron.
There was in the days of Herod, the king of Judaea, a certain priest named Zacharias, of the course of Abia: and his wife was of the daughters of Aaron, and her name was Elisabeth. Luke 1:5
So, we know Elizabeth was a daughter of Aaron, of the Levitical priestly line.
And thou shalt give the Levites unto Aaron and to his sons: they are wholly given unto him out of the children of Israel. Num 3:9
What about Luke 1:36?
And, behold, thy cousin Elisabeth, she hath also conceived a son in her old age: and this is the sixth month with her, who was called barren. Luke 1:36
The word translated "cousin" is syngenes. It means this.
of the same kin, akin to, related by blood
in a wider sense, of the same nation, a fellow countryman -source-
So, they are related in the sense of being Jewish.
And what do we know for a certainty with Mary's tribe?
Concerning his Son Jesus Christ our Lord, which was made of the seed of David according to the flesh; Rom 1:3
Absolutely. Mary was of Judah.
So, clearly Elizabeth was of the Levitical tribe and Mary was of the Judah tribe. They were not related, except as being part of the same nation.
PS. I would guess that those who want Elizabeth and Mary to be cousins has more to do with the question about Jesus' brothers, than about the OP. FWIW.
If I may interrupt so many sapient apologists, my view is that Mary had to be related either to Elizabeth or Zechariah.
No one makes a long and possibly dangerous journey to visit a fellow pregnant countrymen one does not know.
By the way Benedict XVI affirms on his treaty about Jesus Christ that both were indeed related: Jesus Von Nazareth. Beiträge zur Christologie -ISBN 978-84-9055-939-0 for the Spanish edition-
All chapter 2 discuses about this, specially on page 66 is said that Mary and Elizabeth have a blood bond.