The temple at this time was in the southern nation of Judah, not in the northern nation of Israel.
The ten northern tribes seceeded and formed their own nation known as Israel. The king of Israel set up his own centers of worship in Bethel and Dan. He knew that if the people went to Jerusalem to worship, that they would become faithful to the King of Judah, and so they set up their own temples.
The Old Testament implies that there were many shrines both in Israel and in Judah, coexisting with the Temple in Jerusalem, something which archaeology also attests to. Aside from the state-sponsored cultic centers at Dan and Bethel, there were probably also religious activity in places like Gilgal, Beersheba, Lachish, Shiloh, Shechem, Samaria, Hazor, Gezer, Nebo, Arad, Hebron, and Beersheba.
The thing about ancient religion is that there are different levels of cult (a particular group’s enactment of their beliefs and customs), and to some extent this is also true of Israelite religion. First off you have the domestic cult. Although there aren’t too many of them in the archaeological record, some homes had a modest household shrine, perhaps one equipped with simple paraphernalia like miniature altars, lamps, clay figurines or a ‘standing-stone’ (
maṣṣebah) which the family members tended with care and regularity to ensure the family’s well-being. Family and clan tombs (for the Israelites, burial - “to be gathered to one’s fathers” - like most anything was a family affair) could also serve as places of ritual and reverence.
A local cult, meanwhile, is one that is maintained by a community - say, a village or several villages, or neighborhoods in urban areas. Worship sites for local cults seem to have been the
bamoth (“high places”): open-air shrines located upon a natural or an artificial raised area (for example, a hill or a man-made mound or platform) outside a village, where villagers gathered for religious and communal festivals and other events (there was no clear distinction between the two in those days), perhaps equipped with nothing more than an altar (some may have a number of
maṣṣeboth standing erect). A regional cult served an area larger than just a few villages, perhaps a tribal territory; we do not know much about them just as less is known materially about tribes than about villages in ancient Israel.
At the top stands the central cult, in particular the state cult. The Temple of Jerusalem and the sanctuaries of Dan and Bethel are two examples of this official, centralized form of religion. The central cult provides us an example of the interweaving of religion and politics (again, there was no “separation of Church and State” in the ancient world): Jeroboam sets up official sanctuaries in Bethel and Dan, two sites hallowed since ancient times, because he feared that his subjects would switch their allegiance to Judah if they were to go to Jerusalem. Hezekiah and Josiah both enact their religious reforms (centralizing - ‘restoring’ - Yahwistic orthodoxy by removing all unauthorized worship centers) as part of political actions: one can say that both kings ruled in rather politically-troubled times.
The northern nation of Israel would eventually become Samaria, intermarry with the surrounding nations, make alliances with them, and adopt their worship practices, diet and culture. They worshiped the God of Abraham, but did so along side of the Gods of the other nations which surrounded them. They had many priests - priest of the God of Abraham who were appointed by the King, and priests to other Gods.
2 Kings 17: 24-34 is really difficult. For one, Samaritanism as we know it today isn’t really ‘syncrestic’; on the contrary, this Samaritanism, which is really highly conservative seems to be yet another variety of postexilic sectarian Judaism (cf. Josephus,
Antiquities 11.340-345). Not all the people who lived in the northern kingdom were literally exiled (The records of Sargon II indicate that he only deported 27,290 inhabitants); a significant number of northern Israelites were still around (cf. 2 Kings 21:19; 23:26; 2 Chronicles 30; 34:1-7, 9; Jereremiah 41.5). If anything, those who are socially important may have been mainly the only ones who were taken away, which would leave most of the common folk. The imported settlers would have arrived in waves, but are never completely able to overwhelm the native population and on the contrary would have been absorbed into it.