(Note: the Almighty has been elided here not because I think it's necessary, but because some of the people who would like to comment and/or share this feel it's necessary. I do so out of convenience to my neighbors, not personal conviction.)
Had to correct someone's misconception today that the Old Testament is about a fire-and-brimstone G-d who sends plagues and pestilences and smites people, and the New Testament is about a loving G-d who forgives.
It's inaccurate, of course. The two Testaments are much more alike than they are different. If you're going to condemn the Old Testament for condoning slavery, you also need to condemn the New Testament on the same grounds (c.f. Paul's Epistle to Philemon). And if you're going to praise the beauty of the Beatitudes, you also need to note the beauty of the Song of Songs.
Christ was not a pacifist: he explicitly advised his followers that if they should own swords, even going so far as to sell their cloaks in order to get them. And if you're going to complain the Old Testament G-d did a fair bit of smiting, what are we to make of Jesus chasing the moneychangers out of the temple with a whip?
More than that ... there's more than a whiff of outright anti-Semitism in the false distinction between them. There's some sort of inherent claim that the Old Testament is a butcher's manual, and that only the unenlightened or bloody-minded would look to it for moral guidance. That implication is offensive in many different ways.
I don't think all the people who make this claim are anti-Semites. But I do believe they've failed to read the books they're talking about, and are instead parroting an anti-Semitic interpretation of the Bible without ever realizing they've signed on to a falsehood.