Were the israelites monotheistic

Answer 1

they should be, as they are in covenant with Jehovah God. but as history shows, they always search for a new god/belief that is why they break the covenant that they have with their only God, Jehovah.

Answer 2

According to The Bible, Israelites had a monotheistic religion but often strayed from it and engaged in polytheistic behavior.

According to historians, Israelites were monolatrous, meaning that they recognized other gods but only worshiped one, until the Babylonian Exile in 586 BCE.

Answer 3

Yes. The Israelites always worshiped the One God. God wrecked the Egyptian idols (Exodus 12:12) and warned against idolatry (Exodus 22:19). Abraham worshiped "the Lord God of Heaven and Earth" (Genesis 14:22 and 24:3) and complained about the Philistines' lack of fear of God (Genesis 20:11).

(See: A biography of Abraham)

Jacob confiscated the idolatrous images taken from Shechem (Genesis 35:2) and got rid of them (Genesis 35:4); and refrained from invoking the gods of Nahor (Genesis 31:53). Rachel pilfered Laban's statue-images (Genesis 31:19) in order to prevent him from idolatry (Rashi commentary, ibid.). Joseph placed his hope in the God of the Forefathers (Genesis 50:24). Moses characterized the Golden Calf as "a great sin" (Exodus 32:21, 30) and punished the worshipers (Exodus ch.32). During the rest of his lifetime and that of Joshua (Judges 2:7), no incidents of Israelite idolatry were reported.

Shortly before he died, Moses warned the people that he suspected that they would eventually succumb to the lure of the idols (Deuteronomy 29:17). Joshua gave a similar warning (Joshua ch. 24).
These warnings came true. Many of the Israelites went astray after the foreign gods (Judges 2:11). However, the Jews never invented their own idol. It was always the baneful influence of other peoples. And there were times when the entire Israelite nation repented (Judges 2:1-4) and prayed to God (Judges 3:9, 3:15, 6:6, 10:10).
Because of the idol-worship that did happen, ancient images of idols have been found in Israel too. Images of God aren't found because it is forbidden to represent Him through imagery (Deuteronomy 4:15-16).

It should be noted that idolatry was never universal among the Israelites. The tradition of the One God was handed down in every generation, whether by the few or the many; and it is those who handed down that tradition whose beliefs we Jews continue today.

Deborah ascribed victory to God (Judges 4:14), Gideon tore down the idolatrous altar (Judges 6:25-27); Samson prayed to God (Judges 16:28), as did Hannah (1 Samuel 1:11) and Samuel (ibid. 12:18); Eli blessed in the name of God (1 Samuel 2:20), Saul built an altar to God (1 Samuel 14:35); Jonathan ascribed victory to God (1 Samuel 14:12), as did David (1 Samuel 17:46); and Solomon built the Temple for God (1 Kings 8:20). A number of the kings "did what was right in God's eyes": David (1 Kings 15:5), Solomon (see 1 Kings 3:3), Asa (1 Kings 15:11), Yehoshaphat (1 Kings 22:43), Yehu (2 Kings 10:30), Yehoash (2 Kings 12:3), Amatziah (2 Kings 14:3), Azariah (2 Kings 15:3), Yotam (2 Kings 15:34), Hizkiah (2 Kings 18:3), and Josiah (2 Kings 22:2). Even at the height of the unfortunate spread of idolatry among the less-loyal Ten Tribes, there were thousands who remained loyal to God (1 Kings 19:18).
And, of course, the Prophets, who spoke in the name of God and warned against idolatry: Isaiah, Jeremiah, Ezekiel, Hosea and so on.
The sages of the Talmud, who ridiculed idolatry (Megillah 25b), were simply continuing in the tradition of the Prophets whose verses are quoted in that context (ibid.).

See also:

Jewish history timeline