The blood of Jesus cannot save anyone. The blood of Jesus only makes salvation possible by paying for the irrevocable death penalty associated with our past sins (disagreements) before we repented to become holy.
What may believers and non-believers do not understand is that the word sin describes disagreement with God, with His word, or with the record of His word in Moses and the Prophets (Luke 16:29-31).
Both believing and unbelieving men and women disagree with the voice of Jesus of Jesus in Moses and the Prophets according to the Parable of Lazarus and the rich man.
We know that both believing and unbelieving men and women with the Judaism of Jesus in at least one doctrine, which makes us sinners (in disagreement with Jesus).
We read in Ezekiel 33:13 that one sin (disagreement) cancels, voids all our good godly deeds and will cause us to die in the lake of fire with Satan.
Based on Ezekiel 33:13, there is no difference with the believer in Jesus who disagrees with Judaism in one doctrine because they trust or believe that their disagreement is "biblical" and the unbelieving person who disagrees with Judaism in more than one doctrines.
To illustrate one of the many disagreements with Judaism, we can consider the Christian Sabbath Sunday of Christianity versus Saturday, the seventh day Sabbath of Judaism in Moses and the Prophets.
The blood of Jesus cannot save or forgive a "believer" who deliberately does not listen to Moses and the Prophets because the disagreement of the believer with Moses makes the believer an unbelieving believer.
Matthew 26:28 ASV
(28) for this is my blood of the covenant, which is poured out for many unto remission of sins.
Mark 14:24 ASV
(24) And he said unto them, This is my blood of the covenant, which is poured out for many.
Ezekiel 33:13 ASV
(13) When I say to the righteous, that he shall surely live; if he trust to his righteousness, and commit iniquity, none of his righteous deeds shall be remembered; but in his iniquity that he hath committed, therein shall he die.