What you have mentioned in the Muslims’ hatred for Christians and Jews does not represent Islam’s position towards the Abrahamic religions. It is rather the result of political conflicts and manoeuvring, where disputes are made to look like they are between religions. It is unfortunate that politicians use anything they can for their own agendas, even religion, which is a set of values and ideals expressed with affection, peace and justice. The followers of the Abrahamic religions used to live side by side with Muslims in history, and there was peaceful coexistence between them. These relationships were only disturbed by political frictions, and had nothing to do with religion.

We are very surprised by what you mentioned about Muslims’ disrespect for Jesus, peace be upon him. Jesus, peace be upon him, is mentioned in the Holy Qur’an sixteen times, every time with respect and honour. You can refer to the Holy Qur’an and find that out with more depth. Here we mention one of those verses, in which God Almighty said: "And verily We gave unto Moses the Scripture and We caused a train of messengers to follow after him, and We gave unto Jesus, son of Mary, clear proofs..." (Qur’an, 2:87).
The Holy Qur’an speaks of the prophets with great respect and reverence, as it considers them to be purified from any imperfection. The Holy Qur’an pays more respect and gives greater sanctity to the prophets than the Bible does. You can study both books in an objective manner to see this truth clearly.
You can also notice that Muslims do not mention the name of Jesus without saying “peace be upon him”, which is a phrase they do not say but for those who are loyal to God.

Thank you for your communication with us about important and sensitive subjects that relates to the main catholic beliefs. We admire your way in approaching us to learn about the truth from a reliable Islamic source. We advise you to recite the Quran, and refer to it to learn about Muslim beliefs as it is their holy book and they believe in it with total conviction.
Muslims' belief in the divine existence of God is based on proofs and evidences mentioned in a clear way in the Holy Book. They believe that God is one, and He is all surrounding things. He holds all the attributes of goodness. The last two verses from the 59th chapter refer to this when Almighty Allah said: "He is Allah, other than Whom there is no other Allah, the Knower of the Invisible and the Visible. He is the Beneficent, Merciful. He is Allah, the Creator, the Shaper out of naught, the Fashioner. His are the most beautiful names. All that is in the heavens and the earth glorifies Him, and He is the Mighty, the Wise".
When man explores the greatness of this universe - by learning and searching using the modern means, in such a way that is very amazing way, it becomes very clear that Almighty Allah's greatness, capability and encompassing are in an absolute measure and beyond imagination when He created this huge universe with this perfection from nothingness. This, by itself, is sufficient to prove the greatness of the Lord and His absolute capability and wisdom.
Jesus is mentioned in the holy Quran numerous times with respect and appreciation, as he is one of the righteous slaves of God whom He sent unto mankind to guide them to believe in monotheism and to obey His orders and to propagate them. Verses 45-51 from the 3rd chapter refers to this truth when Almighty God said: "(And remember) when the angels said: O Mary! Lo! Allah gives thee glad tidings of a Word from him, whose name is the Messiah, Jesus, son of Mary, illustrious in the world and the Hereafter, and one of those brought near (unto Allah). He will speak unto mankind in his cradle and in his manhood, and he is of the righteous. She said: My Lord! How can I have a child when no man hath touched me? He said: So (it will be). Allah creates what He wills. If He decrees a thing, He saith unto it only: Be! and it is. And He will teach him the Scripture and wisdom, and the Torah and the Gospel, And will make him a messenger unto the Children of Israel, (saying): Lo! I come unto you with a sign from your Lord. Lo! I fashion for you out of clay the likeness of a bird, and I breathe into it and it is a bird, by Allah's leave. I heal him who was born blind, and the leper, and I raise the dead, by Allah's leave. And I announce unto you what ye eat and what ye store up in your houses. Lo! herein verily is a portent for you, if ye are to be believers. And (I come) confirming that which was before me of the Torah, and to make lawful some of that which was forbidden unto you. I come unto you with a sign from your Lord, so keep your duty to Allah and obey me. Lo! Allah is my Lord and your Lord, so worship Him. That is a straight path."
Mary was a righteous woman; Almighty Allah took special care of her when He made one of His great prophets, Zachariah, as her guardian. She was mentioned in the holy Quran numerously like when Almighty Allah said in verses 35-37 from the 3rd chapter:"(Remember) when the wife of 'Imran said: My Lord! I have vowed unto Thee that which is in my womb as a consecrated (offering). Accept it from me. Lo! Thou, only Thou, art the Hearer, the Knower! And when she was delivered she said: My Lord! Lo! I am delivered of a female - Allah knew best of what she was delivered - the male is not as the female; and lo! I have named her Mary, and lo! I crave Thy protection for her and for her offspring from Satan the outcast. And her Lord accepted her with full acceptance and vouchsafed to her a goodly growth; and made Zachariah her guardian. Whenever Zachariah went into the sanctuary where she was, he found that she had food. He said: O Mary! Whence cometh unto thee this (food)? She answered: It is from Allah. Allah gives without measure to whom He will."
The Holy Quran mentioned the birth of Jesus, the son of Mary, and how it was by God's order and not in a usual way of creating the human being, as Mary gave birth to Jesus without marriage as a virgin. She was facing the accusations of the society and mischief makers of committing the sin; but the Almighty Lord proved her innocence when her noble son Jesus spoke in his first hours. This was one of God's miracles and implementation of God's will in a direct way by giving birth to this blessed child. Verses 16-35 from chapter 19, Chapter of Mary, explain this incident when Almighty Allah said: "And make mention of Mary in the Scripture, when she had withdrawn from her people to a chamber looking East, And had chosen seclusion from them. Then We sent unto her Our Spirit and it assumed for her the likeness of a perfect man She said: Lo! I seek refuge in the Beneficent One from thee, if thou art God-fearing. He said: I am only a messenger of thy Lord, that I may bestow on thee a faultless son, She said: How can I have a son when no man hath touched me, neither have I been unchaste? He said: So (it will be). Thy Lord saith: It is easy for Me. And (it will be) that We may make of him a revelation for mankind and a mercy from Us, and it is a thing ordained. And she conceived him, and she withdrew with him to a far place. And the pains of childbirth drove her unto the trunk of the palm-tree. She said: Oh, would that I had died ere this and had become a thing of naught, forgotten! Then (one) cried unto her from below her, saying: Grieve not! Thy Lord hath placed a rivulet beneath thee, And shake the trunk of the palm-tree toward thee, thou wilt cause ripe dates to fall upon thee, So eat and drink and be consoled. And if thou meetest any mortal, say: Lo! I have vowed a fast unto the Beneficent, and I will not speak this day to any man. Then she brought him to her own folk, carrying him. They said: O Mary! Thou hast come with a string thing. O sister of Aaron! Thy father was not a wicked man nor was thy mother a harlot. Then she pointed to him. They said: How can we talk to one who is in the cradle, a young boy? He spake: Lo! I am the slave of Allah. He hath given me the Scripture and hath appointed me a Prophet, And hath made me blessed whosesoever I may be, and hath enjoined upon me prayer and almsgiving so long as I remain alive, And (hath made me) dutiful toward her who bore me, and hath not made me arrogant, unblest. Peace on me the day I was born, and the day I die, and the day I shall be raised alive! Such was Jesus, son of Mary: (this is) a statement of the truth concerning which they doubt. It befitteth not (the Majesty of) Allah that He should take unto Himself a son. Glory be to Him! When He decreeth a thing, He saith unto it only: Be! and it is."
The Bible is amongst the godly revealed books which are mentioned in the holy Quran in many verses. Its aim was to clarify the religious truths and the divine religion of Allah which Jesus brought from Almighty Allah. Verse 46 from chapter 5 refers to this in a clear way when Almighty Lord said: "And We caused Jesus, son of Mary, to follow in their footsteps, confirming that which was (revealed) before him in the Torah, and We bestowed on him the Gospel wherein is guidance and a light, confirming that which was (revealed) before it in the Torah - a guidance and an admonition unto those who ward off (evil)."
Finally we ask the Lord, the Beneficent to guide us all to His right path.