The Mosaic Law is often viewed as God's first attempt at creating a holy people for Himself. Unfortunately, it was a failure. The people couldn't keep all those laws and the sacrifices were never able to remove sin. God needed to do something else, so He sent His Son to be the final sacrifice that would actually work. His people would never have to even try to keep all those Laws again because of Grace, and no further sacrifices would ever be needed. God would have His holy people!
This little scenario is nothing more than a fantasy, a creation of anti-Semitic theology of partial truths. For example, it is true that no one can keep all of God's Laws. This situation was true in the Old Testament days as well as in the New. Grace was man's only hope. Grace was given by God when He gave the people the Laws, so that they knew what was required, and grace was given when the people accepted His covenant. Grace was given when the people made the sacrifices that covered them and allowed them to be in God's presence in the Tabernacle or the Temple. Grace was given during Yom Kippur. Grace was given when Yeshua died and rose again. The penalty for sin was paid. But grace doesn't eliminate the Laws. Yeshua's paying for the penalty of sin doesn't give man a license to violate the Laws. He paid too high a price for man to stomp on the Mosaic Law, which He kept so faithfully and perfectly. He is man's example!
Secondly, it is true that the sacrifices could not remove sin. However, that was never their intended goal. They made atonement, or covered the sin of God's people so that they could enter God's presence. Even the book of Hebrews speaks about the success of the sacrifices.
Hebrews 9:13-14 (KJV)
For if the blood of bulls and of goats, and the ashes of an heifer sprinkling the unclean, sanctifieth to the purifying of the flesh:
How much more shall the blood of Christ, who through the eternal Spirit offered himself without spot to God, purge your conscience from dead works to serve the living God?
If the sacrifices sanctified, or made holy, the flesh, how much more shall the blood of Messiah purge the conscience? Hebrews was making a "light to heavy" comparison. Messiah's sacrifice removed sins, but the sacrifices of bulls and goats also succeeded in covering the people, a lighter result!
Also from Leviticus it is evident that the sacrifices worked exactly as God intended.
Leviticus 9:22-24 (KJV)
And Aaron lifted up his hand toward the people, and blessed them, and came down from offering of the sin offering, and the burnt offering, and peace offerings.
And Moses and Aaron went into the tabernacle of the congregation, and came out, and blessed the people: and the glory of the LORD appeared unto all the people.
And there came a fire out from before the LORD, and consumed upon the altar the burnt offering and the fat: which when all the people saw, they shouted, and fell on their faces.
The last part of this fanciful story is the claim that any who insist upon the obedience to the Mosaic Law are legalists. Somehow it is believed that they are acting as modern day Judaizers (which insisted on following all the minutiae of the Oral Law which were traditions not the Law of God). However, obedience out of love for God can never be legalistic. Rather, disobedience (lawlessness) demonstrates a lack of faith. Disobedience can never result in a holy people!