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The most main stream view that I know of is that they converted to "Hebrew" Monotheism, because Avrahom was a Hebrew.
Avraham followed the faith of Shem and Ever. It was the same monotheism which had been transmitted by Adam in a continuos chain. This is discussed in the beginning of Sefer Raziel HaMalach, Sefer Chanoch, Sefer Noach and is the subject of Sefer Yetzirah.
Starting particularly with the generation of Enosh, many people studied the traditions less and became confused. They started to believe in polytheism and to worship idols. This is also how it is explained by Rambam in chapter 1 of Hilchot Avodat Kochavim in the Mishnah Torah.