There are records of Cyrus also restoring the gods of Babylon that Nabonidus, the last king of the Babylonian Empire, had moved from various Babylonian cities to the capital. That means that he promoted polytheism in that instance as a way to strengthen support from priests of Marduk in Babylon and the priests of Nabu in Sippar. This was undoing the work of Nabonidus in elevating the moon god Sin of the city of Haran over the traditional Babylonian balance of deities/cities.
The Edict of Cyrus that the Chronicler and Ezra write about was also extended to many other nations, not just the exiled Judeans. This casts much doubt as to whether Cyrus was motivated by belief in the One God or by political pragmatism.
From "The Cyrus Cylinder", written by a Babylonian scribe at the beginning of Cyrus's reign:
"When I, Cyrus, entered the city of Babylon peaceably and established to jubilation my royal seat in the Palace of the Ruler, the great Lord Marduk, turned the hearts of many inhabitants of Babylon to love me and I daily sought to worship him. My vast armies paraded peacefully about Babylon, I did not let one frighten the people of Shumer and Akkad. I shepherded in peace the within Babylon and all the sacred cities. The people of Babylon, upon whom he [Nabonidus] against the will of the gods imposed the yoke which did not befit them, I relieved of their sorrows and removed their burden. Upon which Marduk, the great Lord rejoiced at my virtuous deeds and graciously blessed me - Cyrus the King who worships him, Cambyses my son the offspring of my loins, and all my army; and in harmony before him, we praise his supreme divinity."
"All the kings of the world, from the Upper Sea to the Lower Sea, those who inhabit, and all the nomad kings of the West, the tent dwellers, brought their sumptuous gifts into Babylon, and kissed my feet. From Nineveh to the cities of Ashur, Shushan, and Akkad, the Land of Eshnunna and the cities of Zamban, Meturnu, Der and as far as the boundary of the Land of the Gutians [highlanders of Kurdistan], across the Tigris whose temples were destroyed in the distant past, to all of these I have restored and returned their own gods and I have set them up on their eternal seats. I have assembled all their dispersed people and restored them to their habitations."
Cyrus Cylinder - Lines 22-32, translated by Hayim Tadmor in "The Historical Background of the Edict of Cyrus" in "Oz-le-David", Jerusalem, 1964
Source: A History of the Jewish People, edited by H. H. Ben-Sasson