In logic, there are three fundamental laws, without which we literally cannot have a reasonable discussion: The law of identity (a thing is what it is, and isn't what it isn't), the law of non-contradiction (2 opposites cannot be true in the same sense and at the same time), and the law of excluded middle (a statement is true, or its negation is true). To deny any of these three basic laws of thought is literally insane.
What, then, are we to make of the claim that the three "Abrahamic faiths" worship the same god? Answer: Those who make such a statement are literally insane. If you know one thing about Christianity, you know that Christians worship Jesus as God (hence the name CHRIST-ianity). If you know anything about Islam, you know that Muslims do not. This fundamental contradiction necessitates that Christians and Muslims do not worship the same god.
The law of identity comes into play here because it states that a thing is what it is, and isn't what it isn't. The God of the Bible is not the god of the Qur'an. Jesus is God, yet Islam denies this, therefore where X is the God of the Bible, and Y is the god of Islam, X is not Y, and so by claiming X is Y, people like the person in today's screenshot violate the law of identity, thereby making them insane.
The law of non contradiction comes into play here because two opposing statements cannot both be true in the same sense and at the same time. For example, you cannot have a round triangle. If it is a triangle, it's not round. If it's round, it's not a triangle. Islam and Christianity contradict repeatedly when it comes to the nature of God. Is God a Father? Is God triune? Is God internally consistent? Can God lie? Does God love unbelievers? These are all questions to which both religions would give a contradictory answer. Because of this, people who claim Christians and Muslims worship the same god deny the law of non-contradiction, once again making them insane.
The law of excluded middle comes into play here because it states that if a proposition is false, its negation is true (or vice versa). It is false that Jesus, who is the God of the Bible, is the god of Islam, therefore its negation, that being "Muslims do not worship the God of the Bible", is true. Anyone who denies this denies the law of excluded middle.
We see, then, that the claim that Christians and Muslims worship the same god is obviously false, and those who make it are quite literally insane. Yet it's a common claim! There are literally less people who believe chocolate milk comes from brown cows than believe Islam and Christianity are fundamentally the same faith. Thankfully, this insanity can be cured.
See, while Allah does not love the unbeliever (Qur'an 30:45), God demonstrated His love for us in this: While we were yet sinners, Christ died for us (Romans 5:8). Jesus, who according to Islam did not die by crucifixion, but rather was taken up to Allah while it merely looked like Jesus was crucified (Qur'an 4:157-158), did die for our sins according to the Scriptures, and He was buried, and He did rise again the third day according to the Scriptures, He was witnessed alive by many (see 1 Corinthians 15:3-8). Because of this, if you confess with your mouth the Lord Jesus and believe in your heart that God has raised Him from the dead, you will be saved (Romans 10:9). This is a beautiful message of salvation from sin, and reconciliation to God, that is not found in Islam, or indeed any other religion. Christianity is unique. It is unique in its doctrines, unique in its beauty, unique in its power, and unique in its truth.