Both Islam and Judaism agree that there is only one acceptable deen (religion) for all mankind. In Hebrew we have called it yireh shamayim (God fearers, submitters), bnei noah. In Aramaic we called it salamai (the complete ones). In Arabic you call it islam.
Both Islam and Judaism agree that Allah SWT has revealed multiple Shari'ahs (covenants) to groups of people over time. Allah SWT revealed different sets of laws for an Ummah to serve Him in the most perfect way
Where we might differ with some Muslims is that we believe that these Shari'ahs are still active and valid for their Ummah. This is supported by the Qu'ran: "And why do they come to you for a decision while they have the Torah, in which is the Decision of Allah SWT... " (Ma'minim 5.43) and the ahaddith explicitly say that the Mahdi will judge the Jews by the shari'ah of the Torah, Muslims by the shari'ah of the Qur'an etc. Many muslims do not know this. Some draw from Christian theology that the Torah has been abrogated and replaced, but this is not supported by the Qur'an or ahaddith.
"Those who believe, those who are Jews, and the Christians and Sabaeans, all who believe in Allah SWT and the Last Day and act rightly, will have their reward with their Lord. They will feel no fear and will know no sorrow." (Surat Al-Baqara 62)
Rabbi Benamozegh - my teacher - develops the concept of "covenant". He explains that it is like groups of craftsman who gather to build a great palace for a king. Each group thinks that it is the best and most correct, and it is indeed so, because each group is the best and most perfect in its trade. The carpenters are best at what they do. The bricklayers are the best at what they do. The electricians are the best at what they do. What one group teaches as the best way for it to contribute to building the palace, would not be correct for another group. Mixing of talents and techniques would between the groups would reduce the speciality and diversity needed to create the most perfect palace. The diet, clothing and training of each group must necessarily be different. The goal of all of them is the same, and they should compete as if in a race.
Historically, Jews know that for centuries, hundreds of thousands of righteous righteous non-Jews would worship together with the Jews in Jerusalem. The Temple was called by the Prophet "a House of Prayer for All Nations". After the destruction of the the Temple by the Romans, the nation was crushed, the children of Israel fled, and pilgrimages to Jerusalem were forbidden.
Many righteous non-Jews lived in what is now Jordan and Arabia . There was an attempt to rebuild a nation of believers there. However the leadership tried to impose the full the Shari'ah of Moses (pbuh) on the righteous non-Jews, instead of the basic faith of Islam (Bnei Noah). It was supposed to be the "Nation of the LORD" yh-vh-iliyyah, but instead the overburdening and inappropriate application of Torah led to a "nation of ignorance" yahiliyyah.
"Those who follow the apostle, the unlettered Prophet, whom they find mentioned in their own (scriptures),- in the law and the Gospel;- for he commands them what is just and forbids them what is evil; he allows them as lawful what is good (and pure) and prohibits them from what is bad (and impure); He releases them from their heavy burdens and from the yokes that are upon them . So it is those who believe in him, honour him, help him, and follow the light which is sent down with him,- it is they who will prosper" (Surat Al-A'raf 157)
Due to war betwen Rome and Persia, both the Jews and Christians were trying to claim "Arabia" for their own, imposing upon them their version of the Shari'ah of Musa (pbuh) or the Shari'ah of Isa (pbuh) upon an Ummah to which it did not belong. Rabbi Benamozegh taught that the Prophet (pbuh) was sent by Allah SWT to relieve the burden of the nation. To restore the older, original covenant with mankind, and to make clear the path for his Ummah to follow.
In this context we can understand the verses:
And the Jews [who wished to control Arabia] say: The Christians do not follow anything (good) and the Christians [who wished to control Arabia] say: The Jews do not follow anything (good) while they recite the (same) Book. Even thus say those who have no knowledge, like to what they say; so Allah shall judge between them on the day of resurrection in how they are different. (Surat Al-Baqara 113)
And the Jews will not be pleased with you, nor the Christians until you follow their religion. Say: Surely Allah's guidance, that is the (true) guidance. And if you follow their desires after the knowledge that has come to you, you shall have no guardian from Allah, nor any helper. (Surat Al-Baqara 120)
Judaism agrees with this. The great scholar Maimonides taught that Islam is a return to the monotheism of Abraham. God sent [Qur'anic] Islam to help make straight the path for the King Messiah (Mahdi) and to prepare the whole world to serve the God together. (Teshuvot ha-Rambam 2, no. 293)
In general the ahadith clearly indicate the Prophet (pbuh) opposed the mixing of the Mosaic Shari'ah with the Quranic Shari'ah. Judaism also teaches this.
"Narrated Abu Huraira: Allah's Apostle said, "The Jews and the Christians do not dye (their grey hair), so you shall do the opposite of what they do." (Sahih Bukhari Volume 4, Book 56, Number 668)
However, this doesn't mean that one Shari'ah is better or worse than another. It means that each Shari'ah is given to an Ummah.
"From amongst all those ummahs you are among the ummah that has been allotted to me and from amongst all the prophets I am the prophet who hath been assigned to you." (Musnad Ahmad)
Allah SWT could have made mankind one Ummah, with one Shari'ah. But we know that each Ummah has been given its own Shari'ah and that we are to compete, as if in a race, for good deeds and virtue.
"To each among you have we prescribed a Shariah (law) and Minhaj (custom). If Allah had so willed, He could have made you a single Ummah (faith community), but (His plan is) to test you in what He hath given you: so strive as in a race in all virtues. The goal of you all is to Allah; it is He that will show you the truth about the matters in which you are different"; (Al Maeda 48)