How does Judaism view Christianity & Islam?

One of the greatest impacts Christianity has had on Judaism is jealousy...

Deuteronomy 32:21
They [Israel] have moved me [God] to jealousy with that which is not God; they have provoked me to anger with their vanities [idols]: and I will move them to jealousy with those which are not a people [Christians]; I will provoke them to anger with a foolish nation. [Christianity]

Confirmed again in Paul's letter...

Romans 10:19-21
19 - But I say, Did not Israel know? First Moses saith, I will provoke you to jealousy by them that are no people, and by a foolish nation I will anger you.
20 - But Esaias is very bold, and saith, I was found of them [Christians] that sought me not; I was made manifest unto them that asked not after me.
21 - But to Israel he saith, All day long I have stretched forth my hands unto a disobedient and gainsaying people.

As for Islam, their only real link is Ishmael who came forth of works born from their unbelief in God’s promise who had said...

Genesis 15:4
And, behold, the word of the Lord came unto him, saying, This shall not be thine heir; but he that shall come forth out of thine own bowels shall be thine heir.

Whose own bowels [womb] at the time the promise was given was in Sari [Sarah] to whom he had been made one body through marriage...

Genesis 2:23-24
23 - And Adam said, This is now bone of my bones, and flesh of my flesh: she shall be called Woman, because she was taken out of Man.
24 - Therefore shall a man leave his father and his mother, and shall cleave unto his wife: and they shall be one flesh.

Confirmed in...

Genesis 17:15-16
15 - And God said unto Abraham, As for Sarai thy wife, thou shalt not call her name Sarai, but Sarah shall her name be.
16 - And I will bless her, and give thee a son [Isaac] also of her: yea, I will bless her, and she shall be a mother of nations; kings of people shall be of her.

Then Ishmael was the son of works born of unbelief, but Isaac of the faith of faithful Abraham who had believed God’s promise that He would give him a son.

Genesis 21:10-12
10 - Wherefore she said unto Abraham, Cast out this bondwoman [Hagar] and her son [Ishmael]: for the son of this bondwoman shall not be heir with my son, even with Isaac.
11 - And the thing was very grievous in Abraham’s sight because of his son. [Ishmael]
12 - And God said unto Abraham, Let it not be grievous in thy sight because of the lad, and because of thy bondwoman; in all that Sarah hath said unto thee, hearken unto her voice; for in Isaac shall thy seed be called.

And in the fulness of time that Seed would be Jesus Christ a descendant of Abraham, through whom comes all of the promises of the kingdom promised to Abraham.

Galatians 3:13-14
13 - Christ hath redeemed us from the curse of the law, being made a curse for us: for it is written, Cursed is every one that hangeth on a tree:
14 - That the blessing of Abraham might come on the Gentiles through Jesus Christ; that we might receive the promise of the Spirit through faith.

For by the Spirit do we receive all of the promises of the kingdom, now the first fruits but soon the fullness at the appearing of its king Jesus the righteous.