Agreed. Not all sins of ommission are conscious ones. However, IMHO, many are. The good that I knowingly omit to do, because I just don't want to be bothered, or because of personal prejudice, can often do more harm than a sin of commission.
Read, for example, the story of the Good Samaritan (Luke 10: 25-37. It is unique to Luke. Interestingly. Luke, a physician--who could have once been a slave--was a Gentile. Samaritan/Gentiles were not considered to be one with the "chosen ones".)
http://www.biblegateway.com/The Parable of the Good Samaritan
25On one occasion an expert in the law stood up to test Jesus. "Teacher," he asked, "what must I do to inherit eternal life?"
26"What is written in the Law?" he replied. "How do you read it?"
27He answered: " 'Love the Lord your God with all your heart and with all your soul and with all your strength and with all your mind'[c]; and, 'Love your neighbor as yourself.'[d]" [Found in Deuteronomy 6 and Leviticus 19. In Matthew's Gospel, Jesus quote the teaching, himself, as part of his summary of the Ten Commandments.]
28"You have answered correctly," Jesus replied. "Do this and you will live."
29But he wanted to justify himself, so he asked Jesus, "And who is my neighbor?"
30In reply Jesus said: "A man was going down from Jerusalem to Jericho, when he fell into the hands of robbers. They stripped him of his clothes, beat him and went away, leaving him half dead.
JESUS KNOCKED ORGANIZED RELIGION
31A priest happened to be going down the same road, and when he saw the man, he passed by on the other side.
HE ALSO KNOCKED THE BUREAUCRATIC LAITY
32So too, a Levite, when he came to the place and saw him, passed by on the other side.
HE POINTED TO GOOD ACTIONS OF AN OUTSIDER
33But a Samaritan, as he traveled, came where the man was; and when he saw him, he took pity on him. 34He went to him and bandaged his wounds, pouring on oil and wine. Then he put the man on his own donkey, took him to an inn and took care of him. 35The next day he took out two silver coins[e] and gave them to the innkeeper. 'Look after him,' he said, 'and when I return, I will reimburse you for any extra expense you may have.'
36"Which of these three do you think was a neighbor to the man who fell into the hands of robbers?"
37The expert in the law replied, "The one who had mercy on him."
Jesus told him, "Go and do likewise."
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This is the kind of universalism--that good people are to be found in all races and creeds, not just among the chosen ones--is what got Jesus into a lot of trouble with the prejudiced types among his fellow Jews.