It's been long observed that there are no new heresies. Like weeds, they just keep growing back, and while it may look like a different plant, it's the same one as before, with the same roots. See this great breakdown of quite a few old bad ideas.
The one alluded to in the above question, which is based on the idea that the Old and New Testaments are radically different, 'two stories rather than one', is practically the oldest, and is called Marcionism, after the heresiarch Marcion. He first proposed, in the 2nd Century, that the Old Testament was inspired by a completely different god, who was violent and vindictive, from the Father of Our Lord who is the source of Love, and so was to be rejected as having nothing to do with Christ. What makes the question above even more startling is that it I was asked by someone who professes to be a Christian. To be fair, it didn't seem to be their opinion, but they didn't want to upset any 'higher-ups' in their church because they're applying for ministry jobs. I know...that's actually worse, that those in charge of this church could be upset at the idea of the second half of the Bible being somehow related to the first. So much for being 'Bible Christians' eh?
Now, it's unlikely that you'll hear this from a Christian, but it is a common objection from people like Christopher Hitchens, who called Marcion a 'Church Father' (wrong!) in a Channel 4 documentary on the Ten Commandments presented by Anne Widdicombe. What are we to say to this idea, that the God of the OT is cruel and unusual, and the God revealed in Christ is a completely different, much nicer, God?
First, and most important with a lot of heresies, is to point out that it is, in fact, centuries old. Marcionism is almost as old as Christianity itself. So ask, do they really think they're the first person to have 'noticed' that the OT is somewhat different from the NT? Do they also think that no Christians have taken a crack at trying to explain that difference in the last 1,900 years? I suppose we can only hope that their answer is "No."
This brings us to an important principle in apologetics and evangelisation - famously stated as "to study history is to become Catholic." Blessed Newman exhorted his audiences in 'The Present Position of Catholics in England' to "know so much of history that they can defend it." Just as the error is ancient, so is the answer. One of the great things about being Catholic is that you don't have re-invent the wheel when it comes to answering these questions; someone probably wrote a great answer over a thousand years ago.
Which brings us to St. Irenaeus of Lyons, one of the early Fathers of the Church. He was from Asia, but became bishop of Lyons in France, and wrote one of the earliest works of Christian theology called Adversus Haereses, 'Against the Heresies'. He was writing in the middle of the 2nd Century, around the same time as Marcion was spreading his new ideas. Irenaeus deals with Marcionism in a very clear and logical way, espcecially in Book IV, Chapters 32 and 34 (don't worry, they're quite short. Such was Irenaeus' precision when dealing with falsehood!).
In Chapter 32, he relates that a priest who was a disciple of the Apostles, taught his students what the Apostles had taught him i.e. that both testaments (that is, covenants between God and man, and the documents which record them), are given for the good of mankind. The "first testament was not given without reason...[but] foreshadowed the images of those things which exist in the Church...and contained a prophecy of things to come." St. Irenaeus' source, as well as his teaching, is important. Bl. John Henry observed in his studies of the Church Fathers that they primarily relied on Sacred Tradition, the teaching handed on by the Apostles, to refute error, rather than passages of Sacred Scripture because the heretics themselves used Scripture as proof of their false ideas [see Newman's note 2 at the bottom of the page]. Logically, if it didn't come from the Apostles, it didn't come from Christ and the Holy Spirit, and was therefore made up.
Irenaeus does of course use passages of Scripture in defence of the Apostles' teaching. After all, if the point being advanced is the radical disticntion between OT and NT, 'old god' and 'new God', it would be important to demonstrate their unity from the texts in question. In Chapter 34, following on from his point in Ch. 32 regarding the prophecy of the OT, he rhetorically asks the Marcionites who the prophets were announcing if not Christ. If they were inspired by a completely different god as Marcion taught, they must have been anticipating the life of another person, who was a just king, who suffered, died and rose from the dead, while the same events also transpired in the life of Jesus! Clearly, this doesn't hold water. Not content with plain logic, he illustrates the case with quotes from the prophets, the Apostles' letters, and this coup-de-grace from the Lord Himself: "Think not that I have come to destroy the law or the prophets; I came not to destroy, but to fulfill," [Mt 5:17]. Again, if Jesus was the Son of a different God from that which gave the prophets their mission, why would He not come to destroy them and their cruel laws from their cruel God, rather being born a subject of that law?
Once more, we are led to an indispensable principle when trying to unpick any similar difficulties - "What Did Jesus Say?" or WDJS, for short. Alright, I made up the anagram, but the principle still applies. I suppose this is why you're not likely to hear this 'two separate stories' theory from a Christian, because they should know what Jesus thought and taught about this. Further to St. Irenaeus' example, this sprang to my mind from the end of St. Luke's Gospel: "Then he said to them: 'O foolish and slow of heart to believe in all things, which the prophets have spoken. Ought not Christ to have suffered these things and so enter into his glory?' And beginning at Moses and all the prophets, he expounded to them in all the scriptures the things that were concerning him." [Lk 24:25-27, emphasis mine].
Seems pretty clear, right? Without doubt, there are things which are unpalatable or unsavory in the Old Testament to our modern tastes, just as there were to Marcion's tastes, but we risk making a mockery of Christ's mission of love (for He did not need to save us, or prepare us to be saved) if we reject the Old Testament out of hand. Let's encourage those who shy away from embracing the whole Truth, whether Christian or not, to see the object of all the Scriptures for who He really is- the God of Abraham, Isaac and Jacob, made flesh and dwelling among us.