But no one can keep the law - not even Jews. Remember Jesus' parable in Luke 18:9-14. The Pharisee trusted in his own righteousness, whilst the publican threw himself on the mercy of God, knowing full-well he could not keep the law. Yet Jesus stated that the publican was justified, rather than the Pharisee.
9 And he spake this parable unto certain which trusted in themselves that they were righteous, and despised others:
10 Two men went up into the temple to pray; the one a Pharisee, and the other a publican.
11 The Pharisee stood and prayed thus with himself, God, I thank thee, that I am not as other men are, extortioners, unjust, adulterers, or even as this publican.
12 I fast twice in the week, I give tithes of all that I possess.
13 And the publican, standing afar off, would not lift up so much as his eyes unto heaven, but smote upon his breast, saying, God be merciful to me a sinner.
14 I tell you, this man went down to his house justified rather than the other: for every one that exalteth himself shall be abased; and he that humbleth himself shall be exalted.
All Jews sinned during the Old Testament. So how could a Jew with faith in God not do animal sacrifice? I'm not saying it's impossible - maybe the Jew in question was a leper, and not permitted. But in general, faith in God would prompt one to obedience.