"Is it possible to be a Christian and not believe in blood sacrifice -- that is, to not believe that God requires or ever required blood sacrifice to forgive sins?"
No! It is that serious. The verses you quoted were out of context & ignoring the majority of the Bible concerning the NECESSITY of blood sacrifices according to the Old Covenant & especially the New Covenant established by Christ's once for all sacrifice & shedding His own blood to ratify the New Covenant.
To attribute the precious shed blood of the Savior of the world to pagan beliefs & rituals is tantamount to being an unbeliever & trampling the blood of Christ that establishes the New Covenant & blaspheming & bringing the rage of the Holy Spirit.
You are in danger my friend for rejecting what Scripture plainly teaches and what Christianity has taught since the first century. Jesus taught it. The Apostles & writers of the NT taught the necessity of the blood of Christ being sacrificed to atone for the sins of all people.
Heb 10:19-22 Therefore, brothers,
c since we have confidence to ENTER THE HOLY PLACES BY THE BLOOD OF JESUS, by the NEW & living way that He opened for us through the curtain, that is, through his flesh & since we have a great priest over the house of God, let us draw near with a true heart in full assurance of faith, with our hearts SPRINKLED CLEAN from an evil conscience & our bodies washed with pure water.
Heb 10:26-31 For if we go on sinning deliberately after RECEIVING THE KNOWLEDGE OF THE TRUTH, there no longer remains a SACRIFICE FOR SINS, but a fearful expectation of judgment & a fury of fire that will consume the adversaries. Anyone who has SET ASIDE THE LAW OF MOSES DIES WITHOUT MERCY on the evidence of two or three witnesses. How much WORSE punishment, do you think, will be deserved by the one who has trampled underfoot the Son of God & HAS PROFANED THE BLOOD OF THE COVENANT BY WHICH HE WAS SANCTIFIED & has OUTRAGED the Spirit of grace? For we know Him who said, “Vengeance is mine; I will repay.” And again, “The Lord will judge his people.” It is a fearful thing to fall into the hands of the living God.
Heb 9:6-28 These preparations having thus been made, the priests go regularly into the first section, performing their ritual duties, but into the second ONLY the high priest goes & he but ONCE a year & NOT WITHOUT TAKING BLOOD, which he offers for himself & for the unintentional sins of the people.
8By this the Holy Spirit indicates that the way into the holy places is not yet opened as long as the first section is still standing (which is symbolic for the present age). According to this arrangement, gifts & sacrifices are offered that CANNOT PERFECT the CONSCIENCE of the worshiper, but deal only with food & drink & various washings, regulations for the body imposed until the time of reformation.
Redemption Through the Blood of Christ
11But when Christ appeared as a high priest of the good things that have come, then through the greater & more perfect tent (not made with hands, that is, not of this creation)
He entered ONCE FOR ALL into the holy places, not by means of the blood of goats & calves but BY MEANS OF HIS OWN BLOOD, THUS SECURING AN ETERNAL REDEMPTION.
13For if the blood of goats & bulls & the sprinkling of defiled persons with the ashes of a heifer, sanctify for the purification of the flesh, HOW MUCH MORE WILL THE BLOOD OF CHRIST, who through the eternal Spirit OFFERED HIMSELF WITHOUT BLEMISH to God, PURIFY our conscience from dead works to serve the living God.
15ThereforeH e is the MEDIATOR OF A NEW COVENANT, so that those who are called may receive the promised eternal inheritance, since a death has occurred that redeems them from the transgressions committed under the first covenant. For where a will is involved, the death of the one who made it must be established.
17For a will takes effect ONLY AT DEATH, since it is not in force as long as the one who made it is alive. THEREFORE NOT EVEN THE 1ST COVENANT WAS INAUGURATED WITHOUT BLOOD. For when every commandment of the law had been declared by Moses to all the people, he TOOK THE BLOOD of calves & goats, with water & scarlet wool & hyssop & SPRINKLED both the book itself & all the people, saying,
“This is the BLOOD OF THE COVENANT THAT GOD COMMANDED FOR YOU.” And in the SAME WAY HE SPRINKLED WITH THE BLOOD both the tent & all the vessels used in worship. Indeed, under the law ALMOST EVERYTHING IS PURIFIED WITH BLOOD--& WITHOUT THE SHEDDING OF BLOOD--THERE IS NO FORGIVENESS OF SINS.
23Thus it was necessary for the copies of the heavenly things to be purified with these rites, but the heavenly things themselves with better sacrifices than these. For Christ has entered, not into holy places made with hands, which are copies of the true things, but into heaven itself, now to appear in the presence of God on our behalf.
25Nor was it to offer himself repeatedly, as the high priest enters the holy places every year with BLOOD not his own, for then he would have had to suffer repeatedly since the foundation of the world. But as it is, he has appeared ONCE FOR ALL at the end of the ages to PUT AWAY SIN BY THE SACRIFICE OF HIMSELF.
27And just as it is appointed for man to die once & after that comes judgment, so Christ, having been OFFERED ONCE TO BEAR THE SINS OF MANY, will appear a second time, not to deal with sin but to save those who are eagerly waiting for him.
Heb 7:27 Unlike those other high priests, He does not need to offer sacrifices every day. They did this for their own sins first & then for the sins of the people. But Jesus did this ONCE FOR ALL when He offered himself AS THE SACRIFICE FOR THE PEOPLE'S SINS.
Heb 13:12 And so Jesus also suffered outside the city gate, to SANCTIFY THE PEOPLE BY HIS OWN BLOOD.
I Pet 1:18,19 For you know that it was not with perishable things such as silver or gold that you were REDEEMED from the empty way of life you inherited from your forefathers, but with THE PRECIOUS BLOOD OF CHRIST, A LAMB WITHOUT BLEMISH OR SPOT.
John 1:29 The next day John saw Jesus coming toward him and said, "Look, THE LAMB OF GOD, who takes away the sin of the world!
Acts 20:28 Keep watch over yourselves and the entire flock of which the Holy Spirit has made you overseers. Be shepherds of the church of God, which He PURCHASED WITH HIS OWN BLOOD.
Romans 3:25 God presented Him as AN ATONING SACRIFICE THROUGH FAITH IN HIS BLOOD, in order to demonstrate His righteousness, because in His forbearance He had passed over the sins committed beforehand.
I Cor 5:7 Get rid of the old yeast, so that you may be a NEW unleavened batch, as you really are. For Christ, OUR PASSOVER LAMB, HAS BEEN SACRIFICED.
I Pet 1:1,2 Peter, an apostle of Jesus Christ, to the exiles of the Dispersion throughout Pontus, Galatia, Cappadocia, Asia & Bithynia, chosen according to the foreknowledge of God the Father, by the sanctifying work of the Spirit, to obey Jesus Christ AND BE SPRINKLED WITH HIS BLOOD: May grace & peace be yours in the fullest measure.
Heb 12:24 And to Jesus the MEDIATOR OF A NEW COVENANT & TO THE SPRINKLED BLOOD that speaks a better word than the blood of Abel.
Matt 26:27,28 Then He took the cup, gave thanks & gave it to them, saying, “Drink from it, all of you. For this is MY BLOOD, which confirms the COVENANT between God & his people. IT IS POURED OUT AS A SACRIFICE TO FORGIVE THE SINS OF MANY.
Luke 22:20 In the same way, after supper He took the cup, saying, "This cup is THE NEW COVENANT IN MY BLOOD, WHICH IS POURED OUT FOR YOU.
I John 1:6,7 If we say we have fellowship with Him yet walk in the darkness, we lie & do not practice the truth. But if we walk in the light as He Himself is in the light, we have fellowship with one another & THE BLOOD OF JESUS HIS SON CLEANSES US FROM ALL SIN.
Revelation 7:14 Sir," I answered, "you know." So he replied, "These are the ones who have come out of the great tribulation; they have washed their robes & made them white IN THE BLOOD OF THE LAMB.
Leviticus 17:11 For the life of the flesh
is IN THE BLOOD & I have given it to you upon the altar to make an ATONEMENT FOR YOUR SOULS; for it
is THE BLOOD
that maketh an atonement for the soul.
There are many more but I will stop here.