As this episode began, the people were not really asking for a change of gods but rather a new human leader. Moses had borne much of the brunt of Israel's discontent, and now he had disappeared! In their impatience, they wanted to entrust their leadership to one who could make a god. But this highly offended the true God and Moses! To them the golden calf was an attempt to redefine God's nature and control Him according to their desires.
In like manner, the Catholic, Orthodox, and Protestant churches say the ornaments, icons, crucifixes, Madonna statues, and Christmas trees are only to keep God in mind. But this is the same principle involved in Exodus 32! It is not long before people associate the image with God.
In the Golden Calf episode, the first and second commandments were directly broken. Aaron proclaimed it "a feast to the LORD." The churches say, "These things are dedicated to worshipping God." The true God says in verses 7-8 that they had "corrupted themselves . . . and worshipped it." This sounds like today's Christmas observance. The people corrupted themselves by redefining God's nature and His way of worship according to their desires and ends.