I am interested in the views of others, especially Jews, Christians and Muslims on whether they agree with either one or both of the propositions, and if not why not?
No they are NOT sects of Judaism. Christianity is the fulfilment of the Gentiles coming to know God in the Covenant promised to the Jews. Isaac was the Son of the Promise and he was the Son Chosen by God. Christ is the promised Messiah and the Son of God. Islam do not accept the word of God or his word about his people the descendants of Abraham.
Judaism makes it clear there is ONLY ONE GOD and he does not change nor does his word alter.
He has never changed his mind about Abraham, Isaac and Jacob or Jesus Christ the Son of God.
In Dueteronomy
15 The Lord thy God will raise up unto thee a
Prophet from the midst of thee, of thy brethren, like unto me; unto him ye shall hearken;
16 According to all that thou desiredst of the Lord thy God in Horeb in the day of the assembly, saying, Let me not hear again the voice of the Lord my God, neither let me see this great fire any more, that I die not.
17 And the Lord said unto me, They have well spoken that which they have spoken.
18 I will raise them up a Prophet from among their brethren, like unto thee, and will put my words in his mouth; and he shall speak unto them all that I shall command him.
19 And it shall come to pass, that whosoever will not hearken unto my words which he shall speak in my name, I will require it of him.
20 But the prophet, which shall presume to speak a word in my name, which I have not commanded him to speak, or that shall speak in the name of other gods, even that prophet shall die.
Christ is the direct descendant of that line. There is claim that Mahoment claimed he was a descendant of Ishmael.
The Messiah, the true Prophet can only come from the Jewish line through Isaacs descendant. So Christians are Jews by the covenant of Christ in that they are grafted in.
And he said, It is a light thing that thou shouldest be my servant to raise up the tribes of Jacob, and to restore the preserved of Israel: I will also give thee for a light to the Gentiles, that thou mayest be my salvation unto the end of the earth.