Who was Christ to the religious leaders of his day?
A physical descendant of his ancestor, David, one of Israel's first kings, to whose dynasty or lineage most of its subsequent rulers belonged, meant to drive out gentile oppressors, and reinstall the observance of the sacred Mosaic law, thus securing its divine blessings for all upcoming generations.
The question you should have rather asked is:
Who was Christ to Jesus?
To which the answer can be glimpsed from the context of the afore-quoted passages:
Matthew 26:63-65 But Jesus held his peace, And the high priest answered and said unto him, I adjure thee by the living God, that thou tell us whether thou be the Christ, the Son of God. Jesus said unto him, Thou hast said: nevertheless I say unto you, Hereafter shall ye see the Son of man sitting on the right hand of power, and coming in the clouds of heaven. Then the high priest rent his clothes, saying, He hath spoken blasphemy; what further need have we of witnesses? behold, now ye have heard his blasphemy.
Mark 14:61-64 But he held his peace, and answered nothing. Again the high priest asked him, and said unto him, Art thou the Christ, the Son of the Blessed? And Jesus said, I am: and ye shall see the Son of man sitting on the right hand of power, and coming in the clouds of heaven. Then the high priest rent his clothes, and said, What need we any further witnesses? Ye have heard the blasphemy: what think ye? And they all condemned him to be guilty of death.
Luke 22:67-71 Art thou the Christ? tell us. And he said unto them, If I tell you, ye will not believe: And if I also ask you, ye will not answer me, nor let me go. Hereafter shall the Son of man sit on the right hand of the power of God. Then said they all, Art thou then the Son of God? And he said unto them, Ye say that I am. And they said, What need we any further witness? for we ourselves have heard of his own mouth.
John 18:35-37 Pilate answered, Am I a Jew? Thy own nation and the chief priests have delivered thee unto me: what hast thou done? Jesus answered, My kingdom is not of this world: if my kingdom were of this world, then would my servants fight, that I should not be delivered to the Jews: but now is my kingdom not from hence. Pilate therefore said unto him, Art thou a king then? Jesus answered, Thou says that I am a king. To this end was I born, and for this cause came I into the world, that I should bear witness unto the truth. Every one that is of the truth hears my voice.
An earthly ruler, versus a heavenly one; concerning the latter, the Jews were unanimous there could be but one heavenly king, God:
John 8:41 Ye do the deeds of your father. Then said they to him, We be not born of fornication; we have one Father, even God.
just as there could only be one earthly ruler; in this case, the Roman Caesar; indeed, to have suggested otherwise would have been sheer treason:
John 19:15 But they cried out, Away with him, away with him, crucify him. Pilate said unto them, Shall I crucify your King? The chief priests answered, We have no king but Caesar.
As we know from the writings of Josephus, when the latter tried to usurp the authority of the former, riots broke out. Note that the Jews of Christ's time had no problem with earthly fathers, or earthly kings; indeed, Abraham himself is mentioned as a physical ancestor in John 8, referenced earlier; but he did not try to usurp divine fatherhood for himself :
John 8:33 They answered him, We be Abraham's seed, and were never in bondage to any man: how sayest thou, Ye shall be made free? 39 They answered and said unto him, Abraham is our father. Jesus saith unto them, If ye were Abraham's children, ye would do the works of Abraham.
as Jesus is known to have done:
Matthew 23:8-10 But be not ye called Rabbi: for one is your Master, even Christ; and all ye are brethren. And call no man your father upon the earth: for one is your Father, which is in heaven. Neither be ye called masters: for one is your Master, even Christ.
In case the latter is not clear, note that Jesus does not also say call no man your Master upon the earth: for one is your Master, which is in heaven, nor does he merely say call no [one] your father in heaven [other than God]. And if one were to object, saying that it is quite possible to have one heavenly Father, God, and one earthly Master, Christ, remember:
John 3:13 And no man hath ascended up to heaven, but he that came down from heaven, even the Son of man which is in heaven.
We see the same idea reflected later on, in the second greatly-detailed Christian martyrdom, that of Stephen:
Acts 7:55-58 But he, being full of the Holy Ghost, looked up steadfastly into heaven, and saw the glory of God, and Jesus standing on the right hand of God, And said, Behold, I see the heavens opened, and the Son of man standing on the right hand of God. Then they cried out with a loud voice, and stopped their ears, and ran upon him with one accord, And cast him out of the city, and stoned him: and the witnesses laid down their clothes at a young man's feet, whose name was Saul.