Divorce

James Smith asked,
How do Jews interpret Jeremiah 3:8? I've heard many Christians that claim that God divorced Israel.

I cannot speak for Jews in general on this issue. I can say how I understand the Biblical and Rabbinical sources to be saying.

Jeremiah was berating Judah. The Israelite nation had split into two sections. The northern section of the Ten Tribes was taken into Exile. They had become virtually pagans even before their Exile. Their spiritual membership of the Israelite nations was as if to say suspended. Henceforth they were to be counted as Gentiles. In the end times they shall return. The southern section had comprised the Tribes of Judah, and Benjamin, most of Levi, and minority representatives of all the other Tribes. They remained obligated by the commandments. From this section emerged the Jewish People as we know them today.

Jeremiah 3:
8 And I saw that for all the adulteries of faithless Israel, I had sent her away and given her a writ of divorce, yet her treacherous sister Judah did not fear; but she went and was a harlot also.

Here Jeremiah is speaking about both the Ten Tribes (referred to as "Israel" in this case) as juxtaposed to Judah. The Ten Tribes had been "divorced" i.e. they were no longer obligated by the commandments and were to loose awareness of their ancestry. They were to be temporarily considered "Not My People" (cf. Hosea 1:6-10, 5:7, Talmud, Yebamot 17). Judah remained. Judah was still obligated. Judah had seen what had happened to "Israel" but had not learned from it. Jeremiah was upbraiding Judah. [I wrote several books dedicated to this issue, see especially "Hebrew Bride," by Yair Davidiy, 2018.] In the End Times the Lost Ten Tribes of Israel will return and once again acknowledge who they are and accept the commandments.

Ezekiel 37:
 21 Say to them, Thus says the LORD God, Behold, I will take the sons of Israel from among the nations where they have gone, and I will gather them from every side and bring them into their own land; 22 and I will make them one nation in the land, on the mountains of Israel; and one king will be king for all of them; and they will no longer be two nations and no longer be divided into two kingdoms. 23 They will no longer defile themselves with their idols, or with their detestable things, or with any of their transgressions; but I will deliver them from all their dwelling places in which they have sinned, and will cleanse them. And they will be My people, and I will be their God.