Is the religion die rotated in the 1st half of the first year?
Yes it is.
"In the 1st half of each year, each player rotates the dice lying on the cards in his or her respective sets to decrease the faceup number on each of these dice by one."
So you rotate the dice on all cards in your set. If you look at the examples that follow, various players' sets are shown and they all include the religion die. The text of the examples also confirms that the black die on the religion card is rotated at this time.