If salvation comes through faith in Christ, the question that must be answered is “who is this Christ that we have faith in?” If we believe in Him, we believe in His teachings. And what are those teachings?
Thomas Jefferson believed in the historical person named Jesus. Yet he denied so many teachings of Jesus, he disregarded the whole of the Bible. Is that having saving faith?
Mormons believe in Jesus. And they believe He is divine. But they also believe they are all divine. And that the Bible is a corrupted work that must be completed and corrected in the Book of Mormon. Is that having saving faith?
Catholics believe that faith comes from grace which is imparted at Baptism even before a child is capable of comprehending that faith, let alone proclaiming it. Just as long as the Baptism is done in the name of the Trinity. But then Catholics also believe that the entirety of faith is mysterious, and that no proclamation can perfectly convey the infitinely deep contemplations in Christ. Is that saving faith?
Antinomianists believe that faith alone saves, and that people are no longer under the law, so no particular action is necessary to signal that the faith is there. But if Christ says, “do this,” and you refuse to do it, can you say you believe in Him?
Jefferson denied certain Scriptural accounts. Mormons added to Scripture.
The answer to the question in your first sentence is easy: Christ in whom we have faith is the Person described throughout Scripture, without adding or removing anything.