Also, there is only one God, and that is our God. Our God is not the same as the Mormon God, and it's not the same as the Muslim God, and it's not the same as the Jewish God. (the modern Jews are Jews only by name and ethnicity, they don't worship the same God as OT Jews and Hebrews)
You have stepping into philosophically insupportable territory in making this claim. How can what we say about the god to whom we pray possibly affect who that God is? As the OT makes abundantly clear, it is up to God to choose those to whom He listens.
What the Mormons say about God is so utterly incompatible with what we say about Him that it impedes pretty much anything we could do together or hold in discourse. With the Muslims, even more so. But Jesus does hold a central place in Mormon theology so that I can talk about Jesus with them and have some commonality of language, whereas Jesus hardly figures in Islamic thought. With the Mormons I can call Jesus "Savior", and they will in some sense understand and agree (even though their idea of salvation is way off); with the Muslims I cannot. It is important in all of this that both groups add (false) revelation which largely supplants the Orthodox deposit of faith.
The Jews present the opposite side of the coin. Saying that modern Jews are praying to a different God is to my mind nonsensical. It leads one to either making weird (and apparently false) racial claims on the one side, and on the other side stating that for instance the various figures in the gospels are also worshipping the wrong god, when it's quite clear that Jesus is attacking them for worshipping Him wrongly.
I'm sorry, but there is a definite reason that I reject the Protestant definition of Christian. We are the Early Christians, and we are the Early Church, no offense intended, and I'm not meaning to boast or use my "Orthodoxy" (though I'm a poor Orthodox Christian) to argue, but I'm going to say that the members of our Church were the first ones to be called Christians, and so we should let the Church tell us what being a Christian is and what it is not.
It is also blasphemous to say that the Muslims, Mormons and Jews all worship the same God as we do. That is simply NOT true. You absolutely must worship the same God as Christianity. To argue that doctrine, dogmatics, theology, etc... doesn't matter is wrong and that is something I'm not going to sit here and stand for.
I just spent the whole semester taking a class learning about different views of Christ within "Christianity", and I'm going to tell you that there are some brands of "Christianity" that are not Christian at all. To refuse to call Christ God, or to refuse to accept the Holy Trinity is to mean that you are rejecting the essence of Christianity itself.
We were taught in-class that there are some "Christians" who don't believe that any miracles occurred and that all the "miracles", even those by Christ were just metaphors. There are also some "Christians" that don't believe that Christ was a God, and was just a really "holy" man, that is, a moral teacher. There are also some "Christians" that reject 95% of the New Testament, arguing it was all written by the Church, and didn't come from the mouth of Christ himself. I'm sorry, but these beliefs are not Christian.
Doctrine, Dogmatics, Theology, Orthodoxy, Orthopraxis, Faith, Works, it's all a part of being a Christian. To be a Christian doesn't mean you are "good" at it, in fact most of us are very poor at being Christians. But you must affirm not just a belief in Christ, but you must affirm that Christ is God, you must affirm the Holy Trinity. Essentially, you must accept that which is defined in the Nicene Creed, because this is the faith of the Apostles, this is the faith of the Earliest Christians. To be a Christian is much, much more than just a "belief" or "acceptance" of Jesus Christ. This is something that I'm going to have to say should be absolutely rejected by modern Christianity, and is a very unfortunate belief that modern Protestantism has brought to the table.
To illustrate my point, here is a hypothetical situation:
Say I believe in Jesus Christ, and accept him as my Lord and Savior. Yet I also believe that this Jesus Christ is not God himself, but rather a lesser deity. I also believe that he really didn't die on the cross, but that was simply an illusion put forth by Jesus so that people would think he had died, when in reality, he ascended into "heaven" and rules over our world. However, what he did for us, is showed us that every one of us can become deities ourselves. I believe that as long as we live good, moral lives according to how Jesus lived his, then we will attain this godhood. I also believe that there is no Holy Trinity, but rather that the Father is a Force-like entity, and that Jesus was born through this entity. Not only that, but I also believe that the Holy Spirit is the use of this entity, and that through the use of the entity, and your connection with it, that you attain the godlike status that Christ attained. So essentially, if we live moral, "Christ-like" lives, and if we "connect" to this entity (through prayer, good works, etc...) then we are saved from our mortality and our imperfectness (what some call sin) by becoming deities.
Now tell me, is this belief Christian? I'm going to argue that it is not Christian. Just believing in Jesus Christ as your savior, etc... is not the criteria for being a Christian. Nor is just being "Christ-like" because even the non-Christians can be Christ-like.
The Christian faith consists of many aspects, Orthodoxy, Orthopraxis, Dogmatics, Doctrine, Works, Faith etc... We aren't perfect Christians, but that doesn't mean that you can through the baby out with the bathwater and just toss out everything that Christianity stands for just so you can be "tolerant" and "accepting" of any group that wants to call themselves Christian.
I'm not going to stand for this. As much as I love my Protestant brethren, this belief, that to be a Christian is simply to "accept Jesus Christ as your personal Lord and Savior" is nothing but utter bull.
Keep in mind, that I live in an area that is extremely important to Mormons, and I've had many friends that are Mormons. I love them dearly. But I'm not going to refer to them as Christians, because I know what they believe, and although they believe in Jesus Christ, it isn't the same Jesus Christ that Christians worship.
If I sound passionate about this, that is because I am. I'm not suggesting I'm a better Christian than some, I know I'm not. But I am absolutely going to stand against this tendency to try and "blur" the lines between what is being a Christian and what isn't. It is very black and white.
Again, I'm not saying that being a non-Christian condemns you. God saves who he wills to save. Even if Ghandi is saved, that does not mean that his belief system was okay, or that it's okay to be Hindu. Nor does that mean he was a Christian in his earthly life. Christianity does not give you an automatic key to heaven. Being a non-Christian doesn't automatically exclude you.
But we do know that Christianity is the complete truth, and is the correct way to attaining communion with God. We have to stand for Christianity and although we need to be tolerant of other faiths and although we need to be respectful. We need to stand strong against anything that tries to blur the lines and suggest that Christian is a vague term, and we need to stand strong against anything that tries to reduce the Christian faith to just a couple qualifications in order to avoid offending some groups.
Lastly, I'm going to reiterate that I love my Protestant brethren, as well as my Roman Catholic brethren, but I'm going to absolutely stand against anything that tries to blur the lines of Christianity. I love Mormons, Jews and Muslims. But I do stand against Mormonism, Judaism and Islam. (and any other non-Christian faith) There is no way I'm ever going to regard any of these groups as worshiping the same God as I. That is simply just blasphemy and I would argue, is in fact the bad, heretical type of Ecumenism that we need to avoid at all costs.