Abraham is a figure from antiquity; stories about the putative discoverer
of the One God contain material that may date from the third millennium
BCE. His name entered Old English from Hebrew as early as the eleventh
century CE, although the term “Abrahamic” did not appear in its original
sense—“relating to, or characteristic of the biblical patriarch, Abraham”—
until 1699. “Abrahamic” in this book means principally “belonging to the
group of religions comprising Judaism, Christianity, and Islam, which
trace their origin to Abraham,” a twentieth-century usage. This definition
updates the commonplace observation that Judaism, Christianity, and
Islam—the “Abrahamic religions”—are somehow closely related. Not
everyone likes this expression or its categorical implications. Some
scholars object that the term “Abrahamic” can mislead, especially insofar
as it may exaggerate the three religions’ similarities and the likelihood
that Jews, Christians, and Muslims can set their differences aside. Others
regard the categorization itself as incoherent, given adherents’
fundamental divisions over matters such as what scriptures they consider
canonical and how they understand God’s nature.
But relegating Judaism, Christianity, and Islam to separate spheres
discounts their affinities. Even as they strove to differentiate themselves
polemically, they acknowledged that they shared a common deity and took
notice of each other’s sacred texts. By the seventh century BCE, a passage
in the future Jewish Bible already proclaimed: “Hear, O Israel. The LORD
[is] our God, the LORD alone” (Deut. 6:4). Few early Christians spurned
these writings or rejected the God they unveiled. Rather, Christianity
embraced both while advancing a counterclaim: Jews did not worship the
wrong god(s) but had gotten God wrong, failing to recognize His
incarnation. Islam, in turn, accepted Tawrat (the Torah) and Injil (the
Gospel) as valid revelations, but asserted the Quran’s primacy. Muslims
accused Jews and Christians of corrupting their own holy books and
denying that Muhammad was the ultimate prophet, but nonetheless
allowed that their rivals also worshipped the One God. Meanwhile, Jews
looking over their shoulders at Christians and Muslims upheld the
integrity and superiority of their own formulations, as did Christian
apologists (defenders of the faith). These disputes often displayed the
rancor characteristic of civil wars—or frays between members of an
extended religious family.
One can classify Judaism, Christianity, and Islam variously. From one
perspective, they are monotheisms, religions that uphold God’s singularity.
Islam itself provides another view, linking them by a tradition of
continued divine revelation disclosed in scripture and culminating in the
Quran. Muslims regard Jews and Christians as “People of the Book”—a
name that outside observers occasionally apply to Muslims too. As apt as
these designations may be, however, they do not entirely differentiate
these three religions from others. Sikhism and ancient Egyptian Atenism,
for example, also qualify as monotheisms, and Muslims came to include
Zoroastrians and Hindus as other “People of the Book.” The most useful
term for collating Judaism, Christianity, and Islam into a single category is
“Abrahamic,” which distinguishes them by stressing the significance they
accord Abraham: Israel’s founding patriarch for Jews, guarantor of the
covenant for Christians, and a prophet for Muslims. Their Abrahamic
identities unite the religions conceptually, even while frequently
polarizing their adherents.
To observe that Jews, Christians, and Muslims believe they worship the
same God does not imply that their traditions preach the same message.
Although the ethics of the world’s religions may converge, their doctrines,
laws, and mythologies do not. Nevertheless, the fact that Judaism,
Christianity, and Islam so readily reference one another while speaking
about the One God suggests how closely linked they are. They express this
connection in the language of divinity, but its foundations are historical.
More than doctrine or even an overlapping vision of Abraham, they share
an association through time. Hence I approach them as a historian,
respecting their faith commitments without judging them.
(from the preface of Charles L. Cohen's "The Abrahamic Religions; A Very Short Introduction".
The problem is where you draw the line.
If Christians and Muslims don't worship "the same God" (that being the God of Abraham), then do Christians and Jews worship the same God?
Not merely that, do sects within the same Abrahamic religions worship the same God?
Do Orthodox and Hasidic Jews worship the same God? What about their ancient predecessors? Did Pharisees worship the same God that the Sadducees and Essenes worshiped? What about the Samaritans, do they worship the same God?
Do Catholics, Arians, Nestorians, Orthodox, Lutherans, Anglicans, Calvinists, Baptists, Unitarian variants, Pentecostals, Methodists, Evangelicals, Jehovah's Witnesses, Mormons all worship the same God?
Do Sunnis and Shias worship the same God?
All of them believe that they believe in the God of Abraham.
If 1 doesn't equal 1, and a house is not a house, a car is not a car, a bike is not a bike, a cat is not a cat. Then there would be something wrong.