Oh dear.
I don't think that that defence really works. For example, Christianity teaches that God is very definitely a Trinity, while Islam teaches that he very definitely is not. These two things can't both be true. It doesn't make sense to say, for example, that part of God is a Trinity and another part isn't, just as part of an elephant is wrinkly and another part isn't. God isn't supposed to have parts at all. One might say that Christians and Muslims are both just describing God as he appears to them, as best they can, and that might be true, but it would still mean that at least one group of them is mistaken in their description of him.
Seeing as Christians also claim to be monotheist (meaning there is only one God, not three), the Muslims seem to be on the right track. Although, truthfully, Mulsims also have spirits and ghosts, but these obviously arent deities.
Well, the doctrine of the Trinity states that there's only one God too. Obviously the Muslim denial of Trinitarianism is more straightforwardly in line with monotheism, but that doesn't mean that it's impossible consistently to hold the doctrine of the Trinity and be a monotheist. I think the Cappadocians did a pretty good job of it, and so, arguably, did Jonathan Edwards. (Edwards has been regarded, variously, as both a tritheist and a modalist, which is normally a sign that someone's got the balance about right.)
I believe the Muslim objection is not so much with the Trinity as it is with the deification of Jesus, which Islam recognizes as one of the prophets.
Koran 5:73 said:They have certainly disbelieved who say, " Allah is the third of three." And there is no god except one God. And if they do not desist from what they are saying, there will surely afflict the disbelievers among them a painful punishment.
The two are pretty strongly connected. The idea of the Trinity likely wouldn't exist if it didn't provide a framework to explain the Incarnation. And Muslims do tend to object to the Trinity pretty strongly, believing it to be a denial of monotheism.
Yes that is correct. The deification (I learned a new word!) of Jesus is the biggest reason why Muslims dislike Christianity, and they dislike Judaism for not having accepted Jesus as a prophet.
In fact they dislike Jews and Christians so much they are referred to as the people of the Book.
Maybe. But Paul is the earliest Christian writer we have, and he definitely had some notion of the Incarnation (Philippians 2:5-7, off the top of my head. Colossians 1 also has a lot of material to that effect). But then that's not 100% clear from later parts of the New Testament. So perhaps it'd be more accurate to say that there was a time when some Christians did not believe Jesus is God. And as Eran noted, that's effectively how things are today.It is interesting to note that there actually was a time when Christians did not believe Jesus is God.