Why are the women in Matthew's genealogy included?

There are ongoing disagreements about why Matthew refers to Tamar, Rahab, Ruth, and Bathsheba in Matthew 1:3-6. It's sometimes suggested that they're included because of the theme of God's acceptance of Gentiles. That theme is prominent in early Christianity, including in the gospel of Matthew, as the magi in chapter 2 illustrate. But Bathsheba apparently was Jewish. She lived in Isarael. In 2 Samuel 11:3, her father is referred to as Eliam, with no further qualifier, whereas the same verse qualifies Uriah as "the Hittite". See, also, 2 Samuel 23:34. If Ahithophel was the grandfather of Bathsheba, which would be further evidence of her Jewishness, that would help explain why Ahithophel betrayed David (because of what David did to Bathsheba). Matthew 1:16 includes Mary, who was Jewish, in a way similar to how the other women are included earlier. Furthermore, when Bathsheba is referred to in verse 6, she's identified as the wife of Uriah, not "the wife of a Hittite", "the wife of Uriah the Hittite", or some other such thing. And she's referred to as Uriah's wife in a context about giving birth to Solomon after marrying David. She wasn't Uriah's wife at the time, yet Matthew chose to mention that she had been Uriah's wife. The focus seems to be on the adulterous origins of her relationship with David, not any connection to Gentiles. Matthew probably didn't think Ruth was guilty of sexual sin, and he didn't think Mary was, so he didn't think the women had sexual sin in common. Even the women who were sexually immoral were so in significantly different ways. For example, Rahab's background as a prostitute is substantially different than conceiving the child mentioned in the genealogy by means of sexual immorality. It also seems unlikely that the women were all thought to have had a low social status independent of issues like sexual immorality (being born into a disreputable family, being of low economic status, etc.). As explained above, Matthew highlight's Bathsheba's involvement in adultery, which is distinct from the sort of social status issues I just referred to. What's the common thread with these women, then?