I am going to disagree with you here...we see all the time on FR, where one person from one 'Christian' religion will tell another person from another 'Christian' religion that they are not really Christians at all, because their religion is just too different or too weird...according to some of the so-called FR religion experts, one cannot actually be a Christian if the belong to the Mormon religion, or the Christian Scientist religion, or the Jehovahs Witnesses religion, or the Catholic Religion, and on and on and on...yet each one of these religions does exactly as you suggest, they probably do agree on the nature of Jesus Christ and his mission and teachings...
That does not stop one person from one 'Christian' religion telling another person from another 'Christian', religion, that they are not really Christians after all..
I disagree completely with your analysis that there are only minor differences....
If you studied their doctrines, you would find that Mormons, Christian Scientists, and Jehovah's Witnesses differ from Biblical Christianity. In fact, each has its own scripture outside the Bible. Many Christians regard these groups as non-Christian cults. However, most Christians are either Catholic, eastern Orthodox, or Protestant, and those groups all use basically the same Bible and hold to the same creeds. They differ, sometime bitterly, on how the church should be organized and run. That's a human failing. It does not affect the validity or value of essential shared Christian beliefs.
It may be that there is "one true faith", but the evidence is against it. The evidence is that claims to "the Holy Faith" are disputed by 4000+, 43,000+ different sects, according to previous posts. At least 1000+ schisms within Christianity, each making a claim for the "right" church that provides everlasting salvation.
The sheer number of competing claims makes it impossible to choose correctly.
So what we do is to choose a faith community that seems to work for us in our time. It is significant that children are maleable--they grow up in one faith tradition, and only exceptional ones break away.