To clarify the wording of 2 Kings 3:27, although the King James Bible translates this passage as 'indignation, the more common translation is either 'wrath' or 'anger'. For example:
2 Kings 3:27 (NAB): So he took his first-born, his heir apparent, and offered him as a holocaust upon the wall. The wrath against Israel was so great that they gave up the siege and returned to their own land.
Ellicott's Commentary for English Readers says that the phrase 'And great wrath fell upon Israel' always denotes a visitation of Divine wrath, but of course in this case a reference to God's wrath seems incongruous. The footnote in the New American Bible explains that this was probably the wrath of Chemosh, the Moabite god to whom the child was offered. He was feared by the Israelites who lost heart on foreign soil.
This event occurred during the early monarchy, when we now know that the Israelites still believed in the efficacy of several gods(1). When the Moabite king sacrificed his son to Chemosh, the Israelites were sure that Chemosh would come to the aid of the Moabites and that their cause was lost.
(1) Mark S. Smith says in The Early History of God: Yahweh and the Other Deities in Ancient Israel, page 64, that according to the available evidence, Israelite religion in its earliest form did not contrast markedly with the religions of its Levantine neighbours in either number or configuration of deities.