Does the Jewish tradition command Jews to love Muslims, who believe in the same God as the Jews do, as opposed to Christians, who worship avodah zarah (A human being worshipped as an Idol)?
We have a commandment to love G-d, and we are taught that man is created in the Image of G-d. So, first, one could argue that Jews are obligated to love other monotheists, which includes Muslims; I don't think we count that as a commandment, however.
As Double AA notes, we are told to love the "stranger" because we were strangers, and we are enjoined from hating the Edomite or the Egyptian.
Aside from that, however, there is no specific commandment to love anyone but our neighbors (alternatively translated as "fellows", aka other Jews).
For the question to make sense as asked, the chronological history of the world would have to be different. Islam - that is, the religion founded by Muhammad and practiced today by that name - was established in approximately 610CE. Judaism predates Islam by well over 1500 years (depending on when you date the origin of "Judaism").
Based on the answer of @Yishai here: the Torah speaks in several places about loving the stranger (e.g. Leviticus 19:33) and helping him (ibid 25:35, Deuteronomy 14:21).
A non-Jew who fits this category is called a "ger toshav".
Based on the above verses, Rambam (Melachim 10:12) writes that a "ger toshev" has to be treated with the same respect and kindness as a Jew.
The definition of "ger toshav" according to Rambam ( Hil. Oved Kochavim 10:6) is one who accepts the 7 Noahide laws (see here. They are 1) The commitments to uphold social justice 2) A prohibition to blaspheme God 3) A prohibition against idolatry 4) prohibition of several sexual relations: certain forms of incest, homosexuality, and bestiality, 5) prohibition against murder 6) prohibition against theft 7) prohibition to consume limbs severed from a still living creature.)
Is should be noted that if a Muslim were of the opinion that he is required to kill non-Muslims, then he would not be included in those who accept the prohibition of murder.
Assuming that a Muslim accepts these, he ought to be included in the category of ger toshav, and thus Jews would be required to be gracious towards them, as with fellow Jews.
However, Rambam adds another requirement to qualify as a ger toshav. In Hil. Melachim (8:11) he writes:
כָּל הַמְקַבֵּל שֶׁבַע מִצְוֹת וְנִזְהָר לַעֲשׂוֹתָן הֲרֵי זֶה מֵחֲסִידֵי אֻמּוֹת הָעוֹלָם. וְיֵשׁ לוֹ חֵלֶק לָעוֹלָם הַבָּא. וְהוּא שֶׁיְּקַבֵּל אוֹתָן וְיַעֲשֶׂה אוֹתָן מִפְּנֵי שֶׁצִּוָּה בָּהֶן הַקָּדוֹשׁ בָּרוּךְ הוּא בַּתּוֹרָה וְהוֹדִיעָנוּ עַל יְדֵי משֶׁה רַבֵּנוּ שֶׁבְּנֵי נֹחַ מִקֹּדֶם נִצְטַוּוּ בָּהֶן.
Anyone who accepts the 7 commandments and makes sure to perform them is considered one of the righteous members of the nations, and he has a share in the World to Come. But that is if he accepts them and performs them since God commanded them in the Torah and informed us through Moses our master that Noahides are commanded in them.
Thus to qualify, a Muslim would need to not just independently perform these, but also recognize their Mosaic source. I don't know if a Muslim would qualify, given that (please correct me if I am mistaken, they believe that the Torah was superseded by the Qur'an). However, perhaps given that they acknowledge (again, correct me if I am wrong) that Moses was a prophet, then perhaps that suffices, assuming (as specified above) that Muslims concede that aforementioned 7 laws of of Mosaic origin.
We are to love, help, and bless those whom HaShem loves, helps, and blesses. Abraham gave gifts to his 6 sons ( of Keturah ) and sent them east. HaShem rescued Hagar and Y'ShmaEL and blessed them. A Persian King financed the rebuilding of Yerushalayim. Another Persian King favored Hebrews and told them to protect themselves. Y'ShmaEL and his brother Yitsaq both buried their father Abraham. The Quran states that it was only sent to confirm the Tanakh. Not loving Muslims is like not loving Hebrews...same DNA,same blood type...and most important "pure monotheism".