Furthermore according to what I understand from Jewish law, the offspring of a Gentile father and Jewish mother was a Gentile. But the offspring of a Jewish father and Gentile mother was Jewish, and after that birth, the mother was considered to be a daughter of Israel in good standing.
Matthew singles out 4 special women because there "was" something special about all of them.
[Matthew 1:3] Tamar: As I have mentioned previously Tamar was not a Canaanite. Tamar was Hebrew.....and the mother of Zerah and Perez. [At Judah's desire, Er married Tamar, a daughter of Aram, [Genesis 10:23] the son of Shem, but because she was not a Canaanitish woman, his mother used artifices against her, and he did not know her, and an angel of the Lord killed him on the third day after his wedding.] This is quoted from Legends of the Jews Volume II. This is not scripture and I am not intending to imply that it is.
[And in those days Judah went to the house of Shem and took Tamar the daughter of Elam, the son of Shem, for a wife for his first born Er.] This is quoted from The Book of Jasher [Chapter 45:23]. This is also not scripture, but is mentioned in [Joshua 10:13] and [2 Samuel 1:18]. Jasher calls him Elam and the Legend of the Jews call him Aram.....Tamar's father. The "Legend of The Jews" says "a daughter" of Aram....possibly meaning down through his line and not actually his real daughter.
Tamar, being Hebrew, and believing that her father-in-law , Judah, might marry another Canaanite women....(his wife Bath-Shua had died [Genesis 38:12] was attempting to keep the bloodline pure Hebrew. Judah, as a widower, would now certainly be able to marry her...if he desired, but did not. Tamar was also quite well aware of the divine injunction against Israelites marrying Canaanites. [Genesis 24:3] And I will make thee swear by the LORD, the God of heaven, and the God of the earth, that thou shalt not take a wife unto my son of the daughters of the Canaanites, among whom I dwell.
Tamar and Judah's son, Perez, becomes an ancestor of our Lord. Because of the unusual circumstances and the fact that Tamar was already mentioned in Hebrew scriptures....Matthew decides to include her in his genealogy.
You already know why Ruth [Matthew 1:5] would be included in Matthew's Gospel as Samuel (ostensibly) wrote scripture about her. This is the same reason Matthew mentions Rachab [Matthew 1:5] as she was the mother of Boaz....another central figure in that book of scripture...and Rachab would then indeed be a special woman too. It goes without saying that Rachab was an Israelite and not the same person as the "Rahab" of the Book of Joshua. At no place in scripture does it mention the harlot, Rahab....marrying anyone. As I said earlier the similarities of the two names has led some folks into this confusion. The two instances would be separated by at least 120 years anyway.
Finally, Bathsheba [Matthew 1:6]: She also was an Israelite, daughter of Eliam who was the son of Ahithophel, an adviser to King David [2 Samuel 15:12] And Absalom sent for Ahithophel the Gilonite, David's counselor, from his city, even from Giloh, while he offered sacrifices. And the conspiracy was strong; for the people increased continually with Absalom. It is because Bathsheba was the mother of King Solomon that she was given a special place in Matthew's genealogy.
Furthermore according to what I understand from Jewish law, the offspring of a Gentile father and Jewish mother was a Gentile. But the offspring of a Jewish father and Gentile mother was Jewish, and after that birth, the mother was considered to be a daughter of Israel in good standing.
I believe this is Talmudic Law....not Torah. I could be wrong.