In the past we have explained these verses by referring to the word "your," indicating they were not keeping His appointed days. This clearly indicates idolatry. But what if God refers to His true Sabbaths and festivals, but His concern is with the way people kept them?
This is a very distinct possibility. The crowds of people were in a festive mood, yet God rejects their worship. To Him their "holiness" was a sham. Since God calls their sacrifices "futile" and their incense "an abomination," the spiritual basis of their worship must be profane. The broader context shows these people had the morals of alley cats! Their eyes were hot with lust and greed; their fortunes had been built on crime. They were envious, murderous, deceitful, stingy, filled with hate and gossip—yet on the Sabbaths they appeared before God as if everything in their relationship was just fine!
What kind of idea of God had they conceived to think that He would accept such conduct? Their worship merely went through the motions with punctilious observance of the Sabbath and rituals. Obviously, the god they conceived was not the true God because He is more concerned with right relationships than scrupulous regard for ceremony.
They broke both the first and second commandments: They conjured up their own image of God and then worshipped in the name of the true God as they saw fit. Worship is the reaction to one's god at all times and cannot be separated from character and attitudes. The true God cannot be fooled.