Mordecai refused to prostrate himself before Haman, not because he viewed the practice as wrong in itself, but doubtless because this high Persian official was an accursed Amalekite by descent.
Following is a quote from the book "Insight On The Scriptures" and the article on Mordecai--
Refuses to Bow to Haman. Subsequent to this, Haman the Agagite was made prime minister by Ahasuerus, who ordered that all in the king’s gate prostrate themselves before Haman in his newly exalted position. Mordecai staunchly refused to do so and gave as a reason that he was a Jew. (Es 3:1-4) The fact that Mordecai based his action on this reason proves that it had to do with his relationship, as a dedicated Jew, to his God Jehovah. He recognized that prostrating himself before Haman involved more than falling down to the earth for an exalted personage, as Israelites had done in the past, merely acknowledging such a one’s superior position as ruler. (2Sa 14:4; 18:28; 1Ki 1:16) In Haman’s case there was good reason why Mordecai did not bow. Haman was probably an Amalekite, and Jehovah had expressed himself as being at war with Amalek “from generation to generation.” (Ex 17:16--saying: “Because a hand is against the throne of Jah, Jehovah will have war with Am′a·lek from generation to generation.”; see HAMAN.) It was a matter of integrity to God and not a political issue on Mordecai’s part.
Insight On The Scriptures--Mordecai