Three days prior to his festival, the idolater is already focused on his deity, because at this time he begins to search for an animal that is suitable to use as a sacrifice. He, therefore, is likely to pay homage to his deity on the day of the festival for any benefits that have accrued to him from that point onward. A Jew, therefore, may not do business with an idolater during those three days, since he will indirectly cause the idolater to praise the name of his alien god.
Rabbi Yehudah says, "We accept payment from them, since this causes the payer distress," but the Sages reply, "Though it causes him distress now, he rejoices afterward."
Art: The Sacrifice of Pan by Francisco De Goya y Lucientes