How can we refute those who claim Islam is one of the monotheistic religions and that Christians and Jews follow the same teaching?
Islam is one of the three monotheistic religions along with Christianity and Judaism. According to Islamic teachings, the other two while claiming monotheism violate monotheism in a variety of ways.
Christianity does this more than Judaism. Christianity violates monotheism by claiming that God is three in one and by giving the attributes of the God to His creatures. It elevates Jesus, a human being, to the status of God, and exhorts the worship of Jesus, instead of the God of Jesus whom Jesus himself worshipped. This is indeed an obvious violation of monotheistic belief.
In Judaism, the monotheistic belief is also violated by giving God some of the human attributes, though maybe not as gross as in Christianity but nonetheless violations. It is mentioned in the Bible, that God repented for what he thought to do to his people, Children of Israel. God repented - repented to whom?
It is written that God walked into the garden and Adam could hear his footsteps so he hid behind a tree, so God trying to find where Adam is, called out his name, “Adam, where are you?” These kinds of depictions of God are unacceptable. It’s depicting God in human form.
Moreover there is a tradition in Christianity especially among the Catholics who are an earlier version of Christianity, painting God looking like a human being. The Sistine Chapel is a magnificent work, done by one of the great Italian painters who spent years working on it. People go there in pilgrimage to look at this wonderful work - it is a work depicting God creating Adam. There is God sitting on the throne with a big white beard reaching out his hand and there is Adam reaching out his hand. They used this picture in a lot of advertisements later on. It is based on a mistaken idea that God created man in His image meaning that man looks like God. Some groups among the Christians like the Mormons (some Christian groups may not consider them as Christians) - based on this concept have the idea that God is a HUGE man.
There are other references in the bible to Melchisedec (kind of Salem) which again is a violation of monotheism whereby attributes of God are given to His creatures.
“For this Melchisedec, king of Salem, priest of the most high God… Without father, without mother, without descent, having neither beginning of days, nor end of life; but made like unto the Son of God; abideth a priest continually.” 
The correct belief concerning God is that everything besides God is created, they have beginning in time and they have ending in days.
God taught Adam the one true religion, and that’s what He revealed to all of the prophets from Adam to Abraham, Moses, Jesus until the last and final messenger Muhammad (ﷺ). He did not teach different religions as the Bible states, “God is not the author of confusion.”and many different religions would be a basis for confusion. One God who created one world containing one human race – it makes sense that the religion He gave to them was one.
 Book of Exodus, 32:14
 Book of Genesis, 3:8-9
 Book of Hebrews, 7:1 & 3
 1 Corinthians 14:33< Back to Questions