"Jesus Christ the same yesterday, and to day, and for ever"
"For I am the LORD, I change not"
That connection is very explicit throughout all four Gospels, but especially so in John's gospel. On multiple occasions, Jesus describes himself using the clear (to Old Testament readers) label of 'the I AM,' that distinct title God offered Moses at the burning bush when specifically asked "whom shall I say sent me?" The Old Testament God taught Moses the title "I AM" because he knew his people, Israel, would recognize him by that ancient name. The Jews in Jesus' day still knew that sacred title, because they were most offended when Jesus blasphemed God (in their evaluation) by applying it to himself. This is all to show that it is not really controversial to most Christian bible students to state that the Jesus who appears in the New Testament claimed to be the same as the God of Israel, the Creator, Moses, the whole Old Testament, really. While it may be that many careless bible readers mistake the Old Testament God for the one Jesus called 'Father God,' but it is still an error easily corrected by more carefully attending to Jesus' own words about himself. The bible God is one God in both testaments-- Jesus.
The logical contradiction is in the beliefs of those Christians who encourage the perception of Jesus to be one-sided, as in a Jesus who only really is like he was in the New Testament, shorn of all his actions in the Old.
In order to lift the Jesus of the Cross over and above Misogynist Jesus of Deuteronomy 21 (especially verses 10-13), Brutal Warlord Jesus of Phinehas (Numbers 25), and Collateral Damage Jesus presiding over the death of the firstborn sons of Egypt (Exodus 12:29), one has to explain away these statements about God's fundamental nature. Indeed, one must be willing to change, with some justification, the accepted definition of the term 'eternal' to now not include the idea 'unchanging.'
It's fine to state a preference about which actions of God upon which one chooses to dwell. But before one is asked to commit one's entire life to following a person, even if that person makes claims like 'Creator' or 'Savior', one should analyze that person's actions completely. Read the fine print, so to speak.
Jesus so identified himself with his statements and actions in the word of God that he adopted that very phrase to describe himself. Presumably, then, the person who called himself 'The Word of God,' was willing that all his prospective followers would hold him responsible for all divine activity in the only Bible available in Jesus' day, the Old Testament.
Regardless of whether or not his modern followers find the OT Jesus' behavior embarrassing, they still should be able to explain why prospective converts ought to trust in the God of the 'fine print'.